This is the Rubik's Revenge or a 4 by 4 cube.
This is probably the hardest puzzle I own. It's not the most time consuming to solve but there are several tricky parts, including getting the centres in the right place and that bloody parity algorithm. Yes, you know which one I mean.
I have a Rubik's brand one and I imagine the Eastsheen one is a lot better, judging by my Eastsheen 5 by 5 by 5.