I can't even begin to understand how this thing works, let alone how I would even begin to solve it.
Lucky for me Kenneth Brandon (via Geek.com) has done it instead, compressing 7.5 hours of twisting into a 6-minute video.
According to Brandon there are 66.9 quinquaseptuagintacentilliard positions in a 17 by 17 cube, which I'm not sure is even a real word, so let's just say a lot. Apparently, it's not much harder to solve than a normal sized cube, using a reductive method of breaking each 17x17 face into chunks and then solving them in turn. It's "tedious" though, says Brandon.
So you hear that? It's easy! Go get your own and get to it! When you have a free day that is.