This 3D Chess variant is called Rubik Chess, not because Rubik invented it, but because the playing field upon which it is played resembles a Rubik Cube.
 
There are only two types of pieces, Pawn and King. Both King and Pawn move one space in any orthogonal or diagonal direction. The King is not allowed to move to an attacked space.
 
The game is won by checkmating the opponent's King.
 
Happy Hunting.