Cocke was commissioned in the United States Army in 1942 and served in World War II.
At age 29, he became the youngest person to command the Legion, the U.S.' largest wartime veterans' organization.
Cocke was a banking consultant and lobbyist who did considerable work in business management and public relations.
He co-founded Cocke & Phillips International Corporation, a banking consulting and lobbying firm founded in Washington, D.C. After serving as an aide to Secretary of State George Marshall and Secretary of Defense Robert A. Lovett, he was appointed a U.S. delegate to the United Nations General Assembly by President Dwight D. Eisenhower in 1959.
Cocke held a position in the International Bank for Reconstruction and Development during the administrations of Presidents John F. Kennedy and Lyndon B. Johnson.