Here are words to a great cross-centered songs from John Newton. Sovereign grace did this songs on their album title Songs for the Cross-Centered Life which I would recommend if you want to hear songs about the cross. Bob Kauflin worked with these words from Newton on the song The Look:
I saw One hanging on a tree,
In agony and blood,
Who fixed His languid eyes on me,
As near His cross I stood.
Sure, never to my latest breath,
Can I forget that look;
It seemed to charge me with His death,
Though not a word He spoke.
My conscience felt and owned the guilt,
And plunged me in despair,
I saw my sins His blood had spilt,
And helped to nail Him there.
A second look he gave, which said,
"I freely all forgive;
This blood is for thy ransom paid;;
I die that thou mayst live."
Forever etched upon my mind
Is the look of him who died
The lamb I crucified.
And now my life will sing the praise of pure atoning grace
That looked on me and gladly took my place.
Thus, while His death my sin displays
In all its blackest hue,
Such is the mystery of grace,
It seals my pardon too
With pleasing grief and mournful joy
My spirit now is filled
That I should such a life destroy
Yet live by Him I killed
Grace upon grace,