Torque, distance traveled and power consumed
Force x distance equals energy consumed in the exertion of that force to move something that distance.

If the thing is moved in half the time, the energy consumed is the same but, given that power is rate of energy consumed, the power will be double.

For a motor, power is proportional to both torque and speed of rotation so, if a gearbox is used, torque doubles but speed halves therefore power is the same.

Losses in the gearbox and drives alter this a bit but the general principle remains.