A very fun and unique experience, very cool mechanic.
For the second section the player can use bring and use the cubes from before, without ever using the cylinders or spheres. It's good to have many ways to get passed, but it would be interesting if you don't allow the player to use the previous cubes, so that they have to use the cylinders and spheres to get passed in many ways. (Just a suggestion)
Overall a very cool idea and has a lot of potential for a full game.