Everyone knows wind resistance goes up with the square of speed. But few people know how much power is required to increase speed by a given percentage. The answer is simple.

Suppose you're moving along at speed V, air resistance R, requiring power P, for a distance D. How much power does it take to go twice as fast?

At high speeds, air resistance is the dominating factor so we'll ignore all others. Since air resistance goes up with the square of speed, twice the speed means 4 times the air resistance:
As we already know, R is proportional to V squared.
(2V) squared = (2V) * (2V) = 4 * (V * V) = 4 * R

4 times the air resistance means it take 4 times as much thrust (force) to move. 4 times the force over the same distance D is 4 times the work. But if you go twice as fast, you cover distance D in half the time. 4 times the work in half the time is 8 times the power

Thus, power goes up with the cube of speed.

This really puts the lie to a lot of BS about the top speeds of cars and motorcycles.

For example:

If it takes 100 HP to go 140 MPH on a motorcycle, how much power does it take to go 200 MPH?

200 is 1.43 times 140. 1.43 cubed is 2.92. 2.92 times 100 is 292.
So it takes 292 HP, or almost 3 times as much power to go 43% faster.