Reminds me of a 3D 2048 game I made some years back.
https://kshitij-banerjee.github.io/Cubiks-2048/
Check the dismember view I provided (space bar). That open up the cube to give a better spatial understanding of the board.
That is the problem with 3D games, I realized. Trying to visualize is a pain to most people and deviates them from the game. This was my attempt at solving that.
I think in your case, hovering over a cell and highlighting its adjacent numbers might help create better visual understanding of the state.