John Lightfoot on Matthew 27:54

[Truly this was the Son of God.] That is, "This was indeed the Messias." Howsoever the Jews deny the Son of God in that sense in which we own it, that is, as the second Person in the Holy Trinity, yet they acknowledge the Messias for the Son of God (not indeed by nature, but by adoption and deputation; see Matthew 26:63), from those places, 1 Chronicles 17:13; Psalm 2:12, 89:26,27, and such-like. The centurion had learned this from the people by conversing among them, and, seeing the miracles which accompanied the death of Christ, acknowledged him to be the Messias of whom he had heard so many and great things spoken by the Jews. In Luke we have these words spoken by him, "Certainly this was a righteous man": which, I suppose, were not the same with these words before us; but that both they and these were spoken by him, "Certainly this was a righteous man: truly this was the Messias, the Son of God." Such are the words of Nathanael, John 1:49, "Thou art the Son of God; thou art the King of Israel." Peter, when he declared that "Christ was the Son of the living God," Matthew 16:16, spoke this in a more sublime sense than the Jews either owned or knew; as we have said at that place.