This is a very cool concept. The music and graphics really added to the eerieness of the story. Using the cube as both a plot device and the puzzle itself was very innovative and has a lot of potential for possible expansion. The plot about the cube distorting time also plays well to the game mechanic of speeding up the robot, so that was very well done.
I do however think that some of the levels could've been designed better. I'm thinking mostly about level 3, where I managed to collect all 3 items without taking any game actions, just letting the robot run by itself. And in a few other places, all I had to do is leave the robot running and turn back right before it reached the flag to collect the remaining items. In general, the levels felt like they led to more of a brute force approach instead of a carefully considered one. But I understand that given the time constraint, possibly some simplifications were made.