The premise of the game is just like normal chess, which is to "checkmate" the king while protecting your own king! ...Except, the rules are a bit different here.
We know this may be disappointing to some, but pawns can only move forward (two squares on the first move) and capture diagonally. Also, pawns promote on the top and bottom faces of the cube, rather than the first and eight ranks of its sides.
To make things as straightforward as possible, and also to reduce confusion with the already-complicated board, the opponent's king must be captured in order for you to claim the point. As such, kings may be moved into check (such dangerous moves are especially marked by darker squares when previewing a piece's possible moves), and normally-stalemated kings will be forced to move into check. However, in stalemate positions where the king is trapped by its own pieces and cannot legally move anywhere, in check or not, then the position is still a stalemate.
Particularly pertaining to diagonally-moving pieces, it's logically impossible to move past a corner, since that would place said piece on the edge of the board instead of a well-defined square (and that wouldn't a legal position).
The reason for this rule is that the movement pattern for knights is potentially ambiguous, and once a knight is able to cross two or more sides (such as at a corner), then everything become confusing.
There are six sides on a cube, each with unique colors corresponding to that on a Rubik's cube. As such, the letter codes for each side are as follows:
If you ever get confused, just look at a Rubik's cube with the green side facing forwards and the white side facing up.