Great art and sound! The picture was really appealing which is why I played all levels :) I would categorize this as a puzzler and from a design perspective there are therefore a few things I would have changed. 1) you can run around the map anyhow you want and as a result collecting the sides is just a chore that I did at the beginning of each level. I am nut even sure what they are for to be honest. It felt disconnected from the puzzle idea because it had nothing to do with the puzzle itself. Or at least I didn't notice their effect. I would have just removed the sides collection mechanic. Or made it more obvious what they were for. 2) there were not enough consequences in my opinion. I usually just ran around the map until my cube was correctly configured. If a wrong move would prevent me from finishing somehow I would have needed to think more about what I was doing. Here is a an example from the jam that did this better in my opinion (it's not my game): https://itch.io/jam/gmtk-jam-2022/rate/1622626 3) I am also unsure why the cube has 2 valid "solution sides". That just seems like you wanted to make the puzzle simpler to solve. Maybe you could have added something like a "bad side" opposite of the "solution side" and you were not allowed to put the bad side on specific "bad tiles".
Overall I liked the basic idea. The presentation is great. I would have preferred it to be much harder though :) But maybe I just like puzzle games too much :D