So, now my head is starting to hurt. Sorting through this stuff...
It is proportional to the cube of the speed. The force due to drag is proportional to the square. To get power you have to multiply by the rate. Therefore the power is proportional to the cube of the speed.
If it takes 100 hp to go 100 mph then to go 200 it is the ratio of (200/100) cubed times 100 hp or 800 hp.