Not bad and interesting idea, but this game needs a joystick control additionally, for rotating the cube. Besides that, I like the idea, to bring the Rubiks-cube to the C64. One could, for example, combine the joysticks four directional keys with the firebutton and since the steering directions could then always be mapped to the cube's rotation directions, it would naturally be more intuitive, than keyboard controls and likely easier to remember.
One could have a controllable cursor e.g., directly on the cube (a small blinking sign), that the player can move back and forth, through all the single visible parts on the cube, by using the joystick's four directions. Then, depending on, where the player has positioned this cursor on the cube, the user could then rotate that specific section of the cube, by holding down the firebutton and moving in one of the four directions. Then, the player could release the firebutton again, place the cursor somewhere else on the cube and then rotate this part of the cube, and so on and so on. Of course, just a suggestion :-)