Hey Galux.

Think of if you formed an axis and did a rotation, how would the cube not change.

I'll give you a hint: the axis has to go through the origin of the cube, and the points of interest are going to be such that you consider the diagonal pairs and the centre of the cube faces (where there are 6 cube faces and 2 pairs of diagonals).

Thinking about the axis of rotation going through the origin is the best place to start.