"...moving twice the speed takes 4X the energy..."

That's not quite right. The power required to maintain a constant velocity v against a constant drag force of F is P = Fv. With air drag on a car moving at highway speeds, the drag force F actually depends on v: it's proportional to the square of v, i.e. F ~ v^2. All together then:

P ~ v^3

So doubling the speed will increase the required power by a factor of eight.