As this dude demonstrates, it is, in fact, solvable, though it takes him an hour. Or eight years of Ph.D. research plus an hour, but who's counting? Ironically, this is marketed as a "Speed Cube."
Ethan Wolff-Mann is the Gear editor of Supercompressor. He thinks this thing should be free if you can solve it, like one of those giant food challenges. Follow his other thoughts on Twitter @ewolffmann.