It used to be powered by the Tempest, another one of Lament's designs: a pyramidical shaped object which collects the magic of a sorcerer and siphons it off to power the cube.
During the events of Kingdom Of The Wicked, the Tempest was meant replaced by the Accelerator as a power source. However, under Argeddion's control, Lament and his team used the Accelerator to shock Argeddion awake. It is implied later on though, that the Accelerator could still be used to power the Cube.
Valkyrie Cain and Skulduggery Pleasant talked about building a second Cube to hold Darquesse, powered alongside Argeddion's with the Accelerator, so she wouldn't be able to destroy the world. This plan never comes into fruition though, and by The Dying of the Light Darquesse herself states that she is so powerful, she couldn't be contained in a Cube anymore.