It's a banal error. I have explained that already so, sorry if it sounds a bit pedantic.

We assume generally in that kind of problem that engine power here compensate only for the drag. We also assume that drag is the dynamic drag, 0.5*rho*V^2*S (S being the surface of reference).

So in effect, it's correct to assume that when the speed is doubled, the dynamic drag is quadrupled (2V)^2=4V^2.

However, the power is the product of the Effort (here the drag) time the speed.

Hence 0.5*rho*4V^2*S*2*V=0.5*rho*8*S*V^3

Which is 8 time more than before!

That's a bit different