I managed to finish with 2 red, 4 blue and 1 purple.
And I found a way to beat it without collecting any cubes:
https://www.youtube.com/watch?v=uQgGs9Zhlwg

I liked the level in general, but there are some issues I had with it:
I didn't get a good sense of where you are supposed to go.
Most of the level is unnecessary, I was really hoping to get to use all those red and blue cubes.