I honestly really struggled with the controls, especially as the number of faces and the complexity of the puzzles grew. some stuff I found myself wishing for was:
- using the scroll wheel to adjust the field of view
- as others mentioned, snapping to the face that's currently being viewed when changing the camera angle
- a "lock" button that doesn't change the camera angle once you let go of the cube
- generally faster/snappier animations on face change
- some way of showing the whole cube at a glance, like pic related
I liked the concept and, from what I've seen, the puzzles put its potential to good use; in particular you've done a good job of introducing and easing the player into new game elements and tougher puzzles. For this reason I feel like that it's worth focusing development efforts on stuff that complements the puzzles before adding more levels. Good controls are especially important, because the period of time the user takes to input the solution he thought about is essentially downtime between the two fun parts of a puzzle game, thinking and winning, so you want to minimize that.