Wow, this has quite a number of levels, with the third and fourth worlds even exploring brand new mechanics.
So, this game's idea can result in some really clever and unique puzzle solving due to the immense complexity that a rubik's cube generates. As a result, you wind up with puzzles that can be solved in the easy "correct" way vs. the hard way. The danger with this though, is that due to the complexity of the cube, winding up on the hard path just takes deviating from the correct root for a few turns. Suddenly the puzzle becomes much harder, so at that point, might as well hit R. Yet this is of course the most interesting aspect of the game, so it's the kind of thing that has positive and negative consequences.
I think though that as you play more levels, worrying about winding up on the hard path becomes less of a concern, as you realize what the solution probably should look like. You then begin realizing things about the game that result in really interesting revelations about the mechanics. The best design choice here is that the bunny always stays grounded -- turning the cube doesn't change gravity for the bunny. This results in mechanics where you learn that you can never gain height without a staircase, no matter what you do. So it's really neat when you get the world 4 level "Defying gravity", where an egg is floating midair and all you have is a box, and it seems at first that this rule that you thought you learned would be broken somehow (I mean in the end it wasn't really). The simplicity of the puzzle in this case is also what makes it most interesting.
Though I do want to mention that a level like "Cliff Diving" probably should have been placed a bit earlier -- that level teaches you that you can't collect an egg midair in an intuitive way, but already by that point I had tried to do that (probably going on a hard path), and got confused why I couldn't collect the egg. Cliff diving also had an aspect where you had to know to rotate the center piece too, so that made it more complicated, so that's why I say a level like "Cliff Diving", just something really simple so players try and fail to collect the egg in a very clear and obvious setup that shows that that behavior's not a bug or oversight.
But in general the teaching of mechanics is done great and Jon Blow style. Especially in world 3 when portals are introduced, with learning about how portals are active and when they're not intuitively.
Obviously, being prefamiliar with solving rubik's cubes gives a player a pretty big advantage -- they already know certain moves like how to swap in swap out different tiles without moving the ones around them, and they understand that a center, edge, and corner piece are all distinct from each other and can never be in each other's positions. But still, you learn further here that pieces that are subdivided have rules too -- if a square has one corner filled in, that corner will never move, meaning a corner that's toward the center will always be toward the center.
I did have some minor difficulty at times telling if certain blocks were solid or not -- obviously darker squares are background squares, but different colors have different levels of luminosity naturally, so it's not always obvious. I think one minor thing you could do for that would be adding a subtle pattern to distinguish them -- if there's some way to make the non-solid tiles inscribed, or have the solid tiles looks shiny in a consistent way, that might help. Not a huge deal though, especially with the undo button.
I did experience a bug at one point -- I accidentally pressed back at one point (so I was very grateful for the level select), but going back to the level select the worlds seemed to glitch somehow and when I clicked on a level, it took me to the wrong one, in a different world. This persisted even when I went back to the menu and tried again, but when I refreshed the page, it worked (this happened btw on Mt Everest, which was a pretty neat level).
so anyway good job and stuff