In his last written communication Paul commanded Timothy to...

Remember (present imperative - keep on remembering) Jesus Christ, risen from the dead (His divinity), descendant of David (His humanity), according to my gospel (2Ti 2:8-note)

Son - Note that another Greek word huios (5207), translated son, differs from teknon because the latter gives prominence to the fact of birth, whereas huios stresses the dignity and character of the relationship and usually speaks of one who is fully mature. Despite these distinctions, because these words often overlap in meaning and are used seemingly without discrimination, one should not press their semantic differences in every case but allow the context to rule in the interpretation (always a good rule!)

It is interesting to observe that the moment that Paul, the Pharisee of Pharisees, had his eyes opened

"immediately he began to proclaim Jesus in the synagogues, saying, "He is the Son of God." (Acts 9:20)

The gospel is Theo-centric in that God is the ultimate source of salvation, but it is Christocentric in that its executive is the unique Son of God Who cut the covenant in His blood on the Cross.

WHO WAS BORN OF A DESCENDANT OF DAVID: tou genomenou (AMPMSG) ek spermatos Dauid:  (2Sa 7:12, 13, 14, 15, 16; Ps 89:36, 37; Is 9:6, 9:7, Jer 23:5, 6; 33:15, 16, 17, 26; Am 9:11; Mt 1:1, 1:6, 16, 20, 21, 23, 9:27; 12:23; 15:22; 22:42, 43, 44, 45; Lk 1:31, 32, 33, 69, 2:4, 2:5, 2:6; Jn 7:42; Ac 2:30; 13:22, 23; 2Ti 2:8)

See Related Resource: Messianic Prophecies

God's promise to David was

Your house and your kingdom shall endure before Me forever. Your throne shall be established forever. (2Sa 7:16)  (Dr S Lewis Johnson's written or audio discussion of 2 Samuel 7:1, 2,3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17  The Davidic Covenant, part I; The Davidic Covenant, part II)

Isaiah referenced David when he prophesied of the Messiah writing that a

Child will be born to us, a Son will be given to us and the government will rest on His shoulders and His Name will be called Wonderful Counselor, Mighty God, Eternal Father, Prince of Peace (Is 9:6)

"He will reign on David's throne" (NIV, Is 9:7).

Through Jeremiah God promised to

"raise up for David a righteous Branch" (Jer 23:5) Whose "name" is "The LORD our Righteousness" (Jer 23:6)

And so as we open the New Testament, Matthew begins his gospel with "the genealogy of Jesus Christ, the son of David, the son of Abraham" (Mt 1:1)

How fascinating to read that the very ones who had physical sight could not recognize the Messiah as the Son of David (Jn 1:11), but that "two blind men (who) followed Him" were "crying out and saying, "Have mercy on us, Son of David!" (Mt 9:27)  Would it be that all men were physically blind if that opened their hearts to see the "Son of David."

The Jewish crowds wondered "Could it be that Jesus is the Son of David, the Messiah?" (NLT, Mt 12:23) and yet even a Gentile "Canaanite woman" recognized Jesus as the "descendant of David" crying out "Have mercy on me, O Lord, Son of David; my daughter is cruelly demon-possessed." (Mt 15:22)

Paul a former Pharisee knew as did all "good" Pharisees that  "the Messiah" is "The son of David." (Mt 22:42)

Paul reminded Timothy that it was important to

"Remember Jesus Christ, risen from the dead, descendant of David, according to my gospel." (2Ti 2:8-note)

John MacArthur notes that

"Even secular history is replete with reports of Jesus’ life and work. Writing about a.d. 114, the ancient Roman historian Tacitus reported that Jesus was founder of the Christian religion and that He was put to death by Pontius Pilate during the reign of Emperor Tiberius (Annals 15.44). Pliny the Younger wrote a letter to Emperor Trajan on the subject of Jesus Christ and His followers (Letters 10.96–97). Jesus is even mentioned in the Jewish Babylonian Talmud (Sanhedrin 43a, Abodah Zerah 16b-17a)." (MacArthur, J: Romans 1-8. Moody)

The Jewish historian Josephus (circa 90AD) in a brief biographical sketch of Jesus of Nazareth wrote that

"Now there was about this time Jesus, a wise man, if it be lawful to call Him a man: for He was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to Him both many of the Jews and many of the Gentiles. He was Christ. And when Pilate, at the suggestion of the principal men among us, had condemned Him to the cross, those that loved Him at the first did not forsake Him; for He appeared to them alive again the third day as the divine prophets had foretold these and ten thousand other wonderful things concerning Him. And the tribe of Christians so named from Him are not extinct at this day." (Antiquities, vol. 2, book 18, chap 3)

ACCORDING TO THE FLESH: kata sarka: (See Torrey's Topics Human Nature of Christ, The; Prophecies Respecting Christ) (Ro 8:3; 9:5; Ge 3:15; Jn 1:14; Gal 4:4; 1Ti 3:16; 1Jn 4:2, 4:3; 2Jn 1:7)

Flesh (4561)(sarx [word study]) has a range of meanings but here clearly refers to Jesus incarnation as flesh and blood (God "con carne"), fully Man and fully God.

Easton's defines the incarnation as...
 

that act of grace whereby Christ took our human nature into union with his Divine Person, became man. Christ is both God and man. Human attributes and actions are predicated of him, and he of whom they are predicated is God. A Divine Person was united to a human nature (Acts 20:28; Ro. 8:32; 1Cor 2:8; Heb 2:11, 12, 13, 14; 1Ti 3:16; Gal. 4:4, etc.). The union is hypostatical, i.e., is personal; the two natures are not mixed or confounded, and it is perpetual. (See also Person Of Christ, 1-3)

Paul never grew tired of the wonder of "the Word" becoming flesh (Jn 1:14), writing to Timothy that
 

by common confession great is the mystery of godliness: He...was revealed in the flesh... (1Ti 3:16)

The truth of Christ's incarnation is so critical to the gospel that John uses it as a litmus test, declaring
 

"by this you know the Spirit of God: every spirit that confesses that Jesus Christ has come in the flesh is from God and every spirit that does not confess Jesus is not from God..." (1Jn 4:2, 3) adding in his second epistle that "deceivers...do not acknowledge Jesus Christ as coming in the flesh." (2Jn 1:7)

The truth is that
 

Who was declared - Literally who was "marked out Son in power".

As Newell says...

The gospel is all about Christ. Apart from Him, there is no news from heaven but that of coming woe! — Romans Verse-by-Verse

Ryrie adds

Better, designated; i.e., Jesus was designated or proved to be the Son of God by His own resurrection from the dead. (The Ryrie Study Bible: New American Standard Translation: 1995. Moody Publishers)

The Son of God - Morris writes...

While Jesus was fully man--in fact, perfect man, man as God had intended man to be--He was also fully God. This fact was perfectly demonstrated by His bodily resurrection. The power to defeat death and rise again is beyond all human ability. Only the Creator of life, the God who imposed death as the penalty for sin, could defeat death. Christ's bodily resurrection, supported historically as it is by "many infallible proofs" (Acts 1:3) is the crowning proof that He is, indeed, the eternal and unique Son of God.

Declared (3724) (horizo from horos = limit; English "horizon" which is "the apparent line that divides the earth and the sky" which leads to the thought that Jesus is the "line" that divides all time into BC/AD!)

Horizo means to mark out, to bound ("horizon") and figuratively to appoint, decree or specify. It means to be marked out definitely.

In this context horizo signifies that Jesus has been conclusively, irrefutably "marked out" as the "Son of God" by the resurrection. By Jesus' supreme demonstration of His ability to conquer death, a power belonging only to God, He established beyond "all reasonable doubt" (to use a term common in the legal vernacular) that He was indeed God, the Son.

Horizo, is used 8 times in the NT - hover pointer over references  (Lk 22:22; Acts 2:23; 10:42; 11:29; 17:26, 31; Ro 1:4; Heb. 4:7)

The story is told that a certain M. Lepeau complained to Talleyrand that a new religion of his—one he considered a great improvement over Christianity—had failed to catch on with the people. He asked Talleyrand for some suggestions. Talleyrand dryly said,

M. Lepeau, to insure success for your new religion, all you need do is have yourself crucified and then rise from the dead on the third day!

Son of God - Jamieson writes...

Observe how studiously the language changes here. He “was made [says the apostle] of the seed of David, according to the flesh” (Ro 1:3); but He was not made, He was only “declared [or proved] to be the Son of God.” So Jn 1:1, 14, “In the beginning was the Word … and the Word was made flesh”; and Is 9:6, “Unto us a Child is born, unto us a Son is given.” Thus the Sonship of Christ is in no proper sense a born relationship to the Father, as some, otherwise sound divines, conceive of it. By His birth in the flesh, that Sonship, which was essential and uncreated, merely effloresced into palpable manifestation. (See on Lk 1:35; Acts 13:32,33).

With power - Clearly the power capable of raising one from the dead.

Power (1411) (dunamis [word study] from dunamai = to be able, to have power) power especially achieving power. It refers to intrinsic power or inherent ability, the power or ability to carry out some function, the potential for functioning in some way (power, might, strength, ability, capability), the power residing in a thing by virtue of its nature. Dunamis is the implied ability or capacity to perform. It conveys the idea of effective, productive energy, rather than that which is raw and unbridled. Dunamis is the word generally used by Paul of divine energy.

Peter associates Jesus' resurrection with our living hope...

Blessed be the God and Father of our Lord Jesus Christ, who according to His great mercy has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead

Spurgeon adds this pithy practical comment...

Our baptism, solemn as it was, was a great acted falsehood, a living pretense, unless we are dead to our former way of living, and have come to live unto God in a new life altogether, by virtue of the resurrection of Christ from the dead.

Resurrection from the dead - See related resources -

Resurrection (386) (anastasis from anístemi = stand up which in turn is from ana = again + histemi = stand) (word study on anastasis) literally means a standing again. Anastasis as used in Scripture describes one who has come back to life after having died. The undeniable demonstration that Jesus is the Son of God is His resurrection from the dead.

Jesus when asked by the deceptive scribes and Pharisees for a "sign" declared

no sign shall be given to it but the sign of Jonah the prophet for just as JONAH WAS THREE DAYS AND THREE NIGHTS IN THE BELLY OF THE SEA MONSTER, so shall the Son of Man be three days and three nights in the heart of the earth. (Mt 12:39, 40)

Christ's resurrection was the great sign intended to bring conviction and those who would not be convinced by this sign would not be convinced by anything. And so we note the emphasis on the resurrection in the apostle's messages in Acts (Acts 2:32, 3:15, 4:10, 5:30, 31, 32, 10:39, 40, 41, 13:30,31).

The resurrection is in a sense God's "exclamation point" to the good news of resurrection life available in Christ Jesus through the gospel.

The resurrection furnishes the most conclusive and irrefutable evidence of Jesus’ divine Sonship. By the demonstration of His ability to conquer death, a power belonging only to God Himself (the Giver of life), Jesus established beyond all doubt that He was indeed God, the Son.

During the years following the French Revolution, there was a great turning away from the Christian religion. A certain man named La Revilliere concocted a new religion which he thought was far superior to Christianity, but had trouble convincing others to follow him. Seeking help, he went to the great diplomat Charles de Talleyrand for advice. His advice was simple.

"To ensure success for your new religion, all you need to do is have yourself crucified and then rise from the dead on the third day."

He’s right, of course for it is the resurrection which demonstrates forever that Jesus Christ is the Son of God from heaven.

Paul's parting words to the "Epicurean and Stoic philosophers" was to declare that God had "fixed a day in which He will judge the world in righteousness through a Man Whom He has appointed, having furnished proof to all men by raising Him from the dead." Now when they heard of the resurrection of the dead, some began to sneer... (Acts 17:31, 32)

Alexander Maclaren has the following sermon on the Resurrection...

The Witness Of The Resurrection
—Romans 1:4 (R.V.).

IT is a great mistake to treat Paul’s writings, and especially this Epistle, as mere theology. They are the transcript of his life’s experience. As has been well said, the gospel of Paul is an interpretation of the significance of the life and work of Jesus based upon the revelation to him of Jesus as the risen Christ. He believed that he had seen Jesus on the road to Damascus, and it was that appearance which revolutionised his life, turned him from a persecutor into a disciple, and united him with the Apostles as ordained to be a witness with them of the Resurrection. To them all the Resurrection of Jesus was first of all a historical fact appreciated chiefly in its bearing on Him. By degrees they discerned that so transcendent a fact bore in itself a revelation of what would become the experience of all His followers beyond the grave, and a symbol of the present life possible for them. All three of these aspects are plainly declared in Paul’s writings. In our text it is chiefly the first which is made prominent. All that distinguishes Christianity, and makes it worth believing, or mighty, is inseparably connected with the Resurrection.

I. The Resurrection Of Christ Declares His Sonship.

Resurrection and Ascension are inseparably connected. Jesus does not rise to share again in the ills and weariness of humanity. Risen,’ He dieth no more; death hath no more dominion over Him.’ ‘He died unto sin once’; and His risen humanity had nothing in it on which physical death could lay hold. That He should from some secluded dimple on Olivet ascend before the gazing disciples until the bright cloud, which was the symbol of the Divine Presence, received Him out of their sight, was but the end of the process which began unseen in morning twilight. He laid aside the garments of the grave and passed out of the sepulchre which was made sure by the great stone rolled against its mouth. The grand avowal of faith in His Resurrection loses meaning, unless it is completed as Paul completed his ‘yea rather that was raised from the dead,’ with the triumphant ‘who is at the right hand of God.’ Both are supernatural, and the Virgin Birth corresponds at the beginning to the supernatural Resurrection and Ascension at the close. Both such an entrance into the world and such a departure from it, proclaim at once His true humanity, and that ‘this is the Son of God.’

Still further, the Resurrection is God’s solemn’ Amen’ to the tremendous claims which Christ had made. The fact of His Resurrection, indeed, would not declare His divinity; but the Resurrection of One who had spoken such words does. If the Cross and a nameless grave had been the end, what a reductio ad absurdum that would have been to the claims of Jesus to have ever been with the Father and to be doing always the things that pleased Him. The Resurrection is God’s last and loudest proclamation, ‘This is My beloved Son: hear ye Him.’ The Psalmist of old had learned to trust that his sonship and consecration to the Father made it impossible that that Father should leave his soul in Sheol, or suffer one who was knit to Him by such sacred bonds to see corruption; and the unique Sonship and perfect self-consecration of Jesus went down into the grave in the assured confidence, as He Himself declared, that the third day He would rise again. The old alternative seems to retain all its sharp points: Either Christ rose again from the dead, or His claims are a series of blasphemous arrogances and His character irremediably stained.

But we may also remember that Scripture not only represents Christ’s Resurrection as a divine act but also as the act of Christ’s own power. In His earthly life He asserted that His relation both to physical death and to resurrection was an entirely unique one. ‘I have power,’ said He, ‘to lay down my life, and I have power to take it again’; and yet, even in this tremendous instance of self-assertion, He remains the obedient Son, for He goes on to say, ‘This commandment have I received of My Father.’ If these claims are just, then it is vain to stumble at the miracles which Jesus did in His earthly life. If He could strip it off and resume it, then obviously it was not a life like other men’s. The whole phenomenon is supernatural, and we shall not be in the true position to understand and appreciate it and Him until, like the doubting Thomas, we fall at the feet of the risen Son, and breathe out loyalty and worship in that rapturous exclamation, ‘My Lord and my God.’

II. The Resurrection Interprets Christ’s Death.

There is no more striking contrast than that between the absolute non-receptivity of the disciples in regard to all Christ’s plain teachings about His death and their clear perception after Pentecost of the mighty power that lay in it. The very fact that they continued disciples at all, and that there continued to he such a community as the Church, demands their belief in the Resurrection as the only cause which can account for it, If He did not rise from the dead, and if His followers did not know that He did so by the plainest teachings of common-sense, they ought to have scattered, and borne in isolated hearts the bitter memories of disappointed hopes; for if He lay in a nameless grave, and they were not sure that He was risen from the dead, His death would have been a conclusive showing up of the falsity of His claims. In it there would have been no atoning power, no triumph over sin. If the death of Christ were not followed by His Resurrection and Ascension, the whole fabric of Christianity falls to pieces. As the Apostle puts it in his great chapter on resurrection, ‘Ye are yet in your sins.’ The forgiveness which the Gospel holds forth to men does not depend on the mercy of God or on the mere penitence of man, but upon the offering of the one sacrifice for sins in His death, which is justified by His Resurrection as being accepted by God. If we cannot triumphantly proclaim ‘Christ is risen indeed,’ we have nothing worth preaching.

We are told now that the ethics of Christianity are its vital centre, which will stand out more plainly when purified from these mystical doctrines of a Death as the sin-offering for the world, and a Resurrection as the great token that that offering avails. Paul did not think so. To him the morality of the Gospel was all deduced from the life of Christ the Son of God as our Example, and from His death for us which touches men’s hearts and makes obedience to Him our joyful answer to what He has done for us. Christianity is a new thing in the world, not as moral teaching, but as moral power to obey that teaching, and that depends on the Cross interpreted by the Resurrection. If we have only a dead Christ, we have not a living Christianity.

III. Resurrection Points Onwards To Christ’s Coming Again.

Paul at Athens declared in the hearing of supercilious Greek philosophers, that the Jesus, whom he proclaimed to them, was ‘the Man whom God had ordained to judge the world in righteousness,’ and that ‘He had given assurance thereof unto all men, in that He raised Him from the dead.’ The Resurrection was the beginning of the process which, from the human point of view, culminated in the Ascension. Beyond the Ascension stretches the supernatural life of the glorified Son of God. Olivet cannot be the end, and the words of the two men in white apparel who stood amongst the little group of the upward gazing friends, remain as the hope of the Church: ‘This same Jesus shall so come in like manner as ye have seen Him go into heaven.’ That great assurance implies a visible corporeal return locally defined, and having for its purpose to complete the work which Incarnation, Death, Resurrection, and Ascension, each advanced a stage. The Resurrection is the corner-stone of the whole Christian faith. It seals the truths that Jesus is the Son of God with power, that He died for us, that He has ascended on high to prepare a place for us, that He will come again and take us to Himself. If we, by faith in Him, take for ours the women’s greeting on that Easter morning, ‘The Lord hath risen indeed,’ He will come to us with His own greeting, ‘Peace be unto you.’ (Maclaren, A. Expositions of Holy Scripture)

ACCORDING TO THE SPIRIT OF HOLINESS: kata pneuma hagiosunes: (1Pe 1:11; 2Pe 1:21; 2Sa 23:2,  Rev 19:10)

A number of commentators feel the phrase spirit of holiness indicates a spirit or disposition of holiness which characterized Christ spiritually" but John MacArthur (whose interpretation I favor) states that
 

It was the Holy Spirit working in Christ Who accomplished Jesus’ resurrection and every other miracle performed by Him or associated with Him. In the incarnation, Jesus Christ was conceived by the power of the Holy Spirit and was raised from the dead by the power of the Holy Spirit. (Ibid)

Ryrie adds
 

Some understand according to the Spirit of holiness to refer to the Holy Spirit, whereas others consider it a reference to Christ's own holy being. Thus the verse may be understood this way: the resurrection of Jesus is the mighty proof of His deity, and this is declared by the Holy Spirit. (The Ryrie Study Bible: New American Standard Translation: 1995. Moody Publishers)

JESUS CHRIST OUR LORD: Iesou Christou tou kuriou hemon:

What a great name -- Jesus Christ our Lord (Acts 4:12). Newell adds that...
 

Ten times in Romans Paul uses this title, or, “Our Lord Jesus Christ,” that full name beloved by the apostles and all instructed saints from Pentecost onward: for “God hath made Him both Lord and Christ, this Jesus whom ye crucified” (Acts 2:36).  Romans Verse-by-Verse

Spurgeon writes...

What a glorious Lord we serve! He is God's Son: "Jesus Christ our Lord." In his human nature, he is a Man of royal race: "of the seed of David." He was a man, therefore he died: but he rose again, for he was more than man: "declared to be the Son of God with power."
 

He is as much the Son of God as he was the Son of man. The humanity is as true as the divinity, the divinity as true as the humanity.

Jesus is the Hebrew name Yehoshua, (contracted to Joshua or Yeshua = he will save = Yahweh (I Am) + yasha = saves) which means "Jehovah saves".

His full name, The Lord Jesus Christ, is used some 61 times in the NT (click for these verses)

Christ (Christos from the verb chrío meaning to anoint, rub with oil or consecrate to an office) is literally "the anointed" and corresponds to the Hebrew Old Testament term "Messiah" or the Anointed One.

He is Jesus because He saves His people from their sin (Mt 1:21). He is Christ because He has been anointed by God as King and Priest (Rev 19:16, Heb 7:26). He is the Lord because He is God and is the sovereign ruler of the universe (Da 7:27)

Lord (2962) (kurios from kúros = might, power in turn from kuróo = give authority, confirm) describes One who has absolute ownership and uncontrolled power. signifies sovereign power and authority.  In the NT, Jesus is referred to some ten times as Savior and some 700 times as Lord. When the two titles are mentioned together, Lord always precedes Savior.  Jesus is "kurios which describes Him as the supreme in authority, the Owner, the Sovereign Ruler and Master.  Paul adds "our". Is He "your" Lord? Specifically, could someone tell that the Lord Jesus Christ "owns" you by watching the way you live? By observing... the choices you make? ...the language you use? ...the way you love your wife and children? ...the way you treat your employees or co-workers? ...the way you drive on the freeway? ...etc, etc?