If the speed doubles and the force required quadruples, then the power goes up by a factor of eight. This is because power is proportional to force times speed.

The above is true for air resistance and water resistance, where drag is proportional to speed squared. I found a publication linked in this thread that says the same is true of plowing, but another commenter found a paper with experimental results showing the force required increasing much more slowly with speed. If so, plowing is not like fluid resistance and the power required increases even less than the square of the speed.