Really cool concept & the visuals are really cute. Using a rubiks cube as a base for puzzles offer a lot of possibilities in term of level design, which you exploited really really well in the later levels.
in terms of feedbacks, it's hard to think of something that haven't already been said bellow. ^^
My main feedback would be that the controls to rotate & shift the cube only with the mouse is a bit frustrating, making it painful to solve some of the levels where there is a lot of rotations involved. I feel that could discourage most players to go forward in the game, though I have no idea how you could go to improve that part given the large number of inputs that would be needed to control the whole cube with a keyboard or controller (or even just a face). Maybe using both stick of a controller to shift the sides of a face would make it more pleasant to handle but I can see how it would be complicated to handle also.
I also felt that the first levels to introduce how the game works felt a bit too easy & they were many of them. maybe cutting some of them to go faster in the interesting puzzles would be a good idea. but that might be a matter of personal preferance (so don't take only my word for it). Once the first few levels done the difficulty progression is pretty well balanced already. some puzzles could be swapped to make it even more smooth but mostly I didn't really feel like there was huge gaps in term of difficulty.
The sfx and the music are nice. Though I would lower the music a bit by default so you can hear the sfx a bit more. (the click on shifting a face is a satisfying touch)
All in all, It's a really neat concept for a game & with a bit of polish and rework around the contrlos it has a really good potential. Great job :)