Following his declared war on Earth, the Kree scout Noh-Varr was imprisoned in The Cube which he proclaimed as the "start of the new Kree Empire".
During the Civil War, the Cube was used as a villain correction facility placed by S.H.I.E.L.D.
By the time the Secret Invasion hit Earth, Noh-Varr had assumed control of the entire facility and had become it's self-appointed Warden.
Following Norman Osborn's acension to power, Noh-Varr became Captain Marvel and his duties meant he was no longer incarcerated. The Cube instead became the headquarters to Osborn's black-ops Thunderbolts squad.