While the NASB text reads "who was declared the Son of God…" as do many other versions, the Greek text is better translated as "who was appointed the Son of God…."
The prevalent view of the two descriptive statements in verses 3 and 4 of Romans chapter 1 is that they describe the human and divine natures of Christ. In this view, the first of these descriptive statements, "who was born of a descendant of David according to the flesh," is taken to be a reference to our Lord's human nature. Likewise, in verse four, the second statement, "who was declared the Son of God with power by the resurrection from the dead, according to the Spirit of holiness," is seen as a reference to His deity. If this were Paul's intent, he is saying that the subject of the gospel is perfectly human, a descendant of David, and fully divine, as proven by the resurrection from the dead.
While one must hold unreservedly to the full deity and perfect humanity of our Lord, it is better to see Paul’s purpose to declare Jesus as the Messiah, fulfilling the promises made beforehand in the Scriptures. Let it not be doubted or questioned that our Lord is completely and perfectly human and at the same time fully divine. This truth must not be compromised. It is glimpsed in these verses, but only indirectly, for it is not the apostle Paul’s intention to declare this particular truth. His purpose instead is to declare that the subject of the gospel is the person of the Messiah, that He is qualified both physically and spiritually, that He has been appointed to this office, that He is in truth none other than Jesus Christ our Lord.
For a much fuller discussion of this issue, especially how it relates to the book of Romans, see the discussion by the author in The Sonship of our Lord and Our Adoption as Children of God.