Not a bad idea! In a way it kind of gave me mortol (ufo 50) vibes mechanically speaking. I did get stuck in level 3 since for some reason the cube didn't want to jump while half on top of another while before this wasn't an issue. It might also be a nice idea to instead of a full retry button that resets all your progress in the level you also have an additional undo button that would remove your latest cube (since sometimes I'd block my path with one cube and have to reset the entire level). The levels are failry short however so this is not really that big of a problem.
The "clinging" to the cubes also felt a bit strange sometimes as it did cause me to miss the timer a few times and then have to reset but it was a pretty nice feature to be able to build staircases in mid air.
Overall a nice concept.