Cone received many degrees, they include; Bachelor of Arts, Master of Arts and Doctor of Philosophy, all of which he pursued at the University of Iowa. He went on to, in later years, obtain a Doctor of letters of the University of Kentucky.
Cone taught history at Allegheny College and after becoming research assistant at Iowa History Society. After he left this position to become the assistant professor of history at Louisiana State University. leaving this University and joining the University of Kentucky he joined the faculty and went on to become the professor of history. in the same Period, he also took the position of department chairman at the University.
Being a Roman Catholic, Cone was a member of various religious societies and associations
Carl Cone married Mary Louise Regan on December 20, 1942. They had one child named Timothy.