Cocke was born in Brunswick in Nottoway County in the Colony of Virginia in 1772, the eldest son of frontiersman and future senator, William Cocke, and wife Mary (Maclin) Cocke. While still a young child, he moved with his parents across the Appalachian Mountains to what is now Tennessee, where his father was active in the State of Franklin movement.
Cocke was born in Brunswick, Virginia Colony, in 1772, as the eldest son of William Cocke, a frontiersman and future senator, and Mary (Maclin) Cocke. As a young child, he moved with his parents to Tennessee, where his father was involved in the State of Franklin movement.