I'm familiar with tetris-like puzzle games (best way I could describe the shape fitting mechanic), but I love how this game manages to take a basic puzzle concept and make it more interesting! There are a variety of ways you can approach each level, which is something I greatly appreciate in puzzle games. One thing I would suggest is maybe adding some indication of how many levels there are or some sign of general progression.
Also, I can't help but think how fun this would be in a 3D cube layout. Maybe this could be implemented in an extra challenge mode in the future ;)
Great work overall! (P.S. the sound effects are very satisfying to listen to)