Are there any "secret" rooms that contain cube bits?

Solution 1:

It's the owls. You must find the four owls, and enter their secret room, that has one cube bit, and also an anti-cube.

This is the only secret room in the game that has a regular cube bit inside it.

This seems like the designer's way of ensuring that everyone who completes the game is, at the very least, aware of the existence of anti-cubes.

owl secret room on the world map

owl secret room detail