Okay. What do we have here? Cube - three dimensional object of equal side. Also a number to the power of itself three times.

... here-in lies the answer.

Now as to the rest, if I didn't include some other "inside" information to throw you off (or is that to alert others?) it wouldn't be like playing a combination tic-tac-toe and three dimensional chess anymore, now would it?

If you need anymore help I'll mail you one.