"That's When Your Heartaches Begin" is a song recorded by Elvis Presley on at least three occasions, most the notably the first time in July 1953, when it was one of the two first songs recorded by Presley at Sun Records for a demo acetate he allegedly gave to his mother as a birthday present.

While the song did not see any fame until Presley's recordings in the 50s, the song was actually written in 1937 by Fred Fisher, William Raskin and Billy Hill. On July 18, 1953, a young Elvis Presley entered Sun Records in Memphis, where he paid $3.98 for enough studio time to record a double-sided acetate single. On the A-side, he recorded "My Happiness", later made famous by Connie Francis in 1958, while he recorded "That's When Your Heartaches Begin" for the B-side.

He would later revisit the song on at least two occasions, the first during the famous Million Dollar Quartet sessions on December 4, 1956, and the second when he re-recorded the song in January 1957 as a B-side to All Shook Up".
~Source Wikipedia