Saw this on the speedsolving forum. I don't know much about commutators, but this looks like a nice challenge. In fact, someone may have solved it and wanted to make it his PHD publication.
What do you think?
It's trivial to prove impossible by counter-example unless further restrictions are placed on what is meant by "even permutation". For example, on a Helicopter cube the sequence [RU FU]x3 performs an even permutation of the whole puzzle (even though it's odd for each orbit) and it can't be resolved via a commutator or any sequence of only commutators.