Romans 5:8: "but God shows his love for us in that while we were still sinners, Christ died for us."
1 John 4:9-10: "9 In this the love of God was made manifest among us, that God sent his only Son into the world, so that we might live through him. 10 In this is love, not that we have loved God but that he loved us and sent his Son to be the propitiation for our sins."
John 15:13: "'Greater love has no one than this, that someone lay down his life for his friends.'"
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The first two citations (Romans 5:8 and 1 John 4:9-10) appear throughout the first three verses, in which the speaker/singer "wonder[s] much at His love / As He hung on the tree" and "bled and died" for our sins.
The beginning of the fourth verse ("What love is this? Greater love / No one has ever known.") doesn't exactly come from John 15:13 but clearly references it.