Getting into the intricacies of Power verses Energy ...
DE - quite correct - the POWER does increase more than the square of the velocity ...Power goes up by the CUBE of the speed - (which I believe to be fully in line with your 'more molecules per second' coupled with the Energy going up with the square.)
Formula for Calculating the Wind Power Produced
Wind Power Generation
The formula used to calculate the wind power produced by a wind turbine or windmill is the following:
P = c x d x (D^2) x (v^3)
P: Power produced (mechanical) (Watts [W])
c: constant
d: density of wind (kilograms per cubic meter [kg/m^3])
D: turbine blade diameter (meter [m])
v: velocity of wind (meters per second [m/s^2]
http://www.brighthub.com/environment/renewable-energy/articles/103592.aspx
Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good ...