Summary: Considering the hymnody of the faithful, what is the meaning of the hymn Paul cites in this particular text? How does this build the saints today?
“The saying is trustworthy, for:
If we have died with him, we will also live with him;
if we endure, we will also reign with him;
if we deny him, he also will deny us;
if we are faithless, he remains faithful—
for he cannot deny himself.” 
I must believe that the Apostle Paul enjoyed singing. I will be so bold as to suggest that he loved singing. Recall that Paul urged believers, “Let the word of Christ dwell in you richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God” [COLOSSIANS 3:16].
A similar injunction is found in yet another letter Paul wrote. The Ephesian Letter contains this admonition to the people of God, “Do not be foolish, but understand what the will of the Lord is. And do not get drunk with wine, for that is debauchery, but be filled with the Spirit, addressing one another in psalms and hymns and spiritual songs, singing and making melody to the Lord with your heart, giving thanks always and for everything to God the Father in the name of our Lord Jesus Christ, submitting to one another out of reverence for Christ” [EPHESIANS 5:17-21].
These portions of the Word undoubtedly indicate Paul’s doctrinal position. However, many people have difficulty walking in synchrony with their talk. Paul didn’t have that problem. When gaoled in Philippi, the response of the Apostle, together with Silas, was to put into practise what he taught in his letters. Doctor Luke states that following a severe beating, being pinioned in stocks and incarcerated the missionaries serenaded the residents of the jail with hymns. “About midnight Paul and Silas were praying and singing hymns to God” [ACTS 16:25a]. The response was sufficiently out of character for most individuals who were imprisoned that all listened. The Word tells us, “The prisoners were listening to them” [ACTS 16:25b].
The ancient hymnody is not so well known today, but some limited insight into the hymns that the Apostles sung is provided through reviewing Paul’s writings. On several occasions Paul cites portions of what appear to have been hymns that would have been sung. These citations appear to have been sufficiently common that he assumes that readers will instantly recognise the song. A few examples will suffice to demonstrate what I mean.
In the early verses of Colossian Letter, Paul cites a hymn, writing about the Son of God, “He is the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. And he is before all things, and in him all things hold together. And he is the head of the body, the church. He is the beginning, the firstborn from the dead, that in everything he might be preeminent. For in him all the fullness of God was pleased to dwell, and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross” [COLOSSIANS 1:15-11].
Again, in the Letter to Roman Christians, the Apostle cites strophes from at least one, and possibly from two hymns. The appropriate verses citing the hymn(s) read thusly,
“For who has known the mind of the Lord,
or who has been his counselor?”
“Or who has given a gift to him
that he might be repaid?”
[ROMANS 11:34, 35]
Earlier in our studies through these Pastoral Letters we saw another instance where the Apostle clearly cited a hymn known at least to Timothy. The hymn speaks of the Son of God.
“He was manifested in the flesh,
vindicated by the Spirit,
seen by angels,
proclaimed among the nations,
believed on in the world,
taken up in glory.”
Recently, a musician has set this hymn to music, permitting us to imagine what perhaps was heard among the early churches. 
One final citation will suffice. Writing the Philippian congregation, Paul cites what appears to have been a hymn when he writes of Jesus, “Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross. Therefore God has highly exalted him and bestowed on him the name that is above every name, so that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father” [PHILIPPIANS 2:5-11]. Though the verses are easily recognised, many modern believers would not connect them to a hymn. However, it is quite likely that these verses were sung during services among the early congregations.