Skilling's Compound of 6 Cubes
I came up with this idea somewhere in 1999. Later on I found out that that J. Skilling of Cambridge, England, already found this model in 1975. It has a rotation freedom, though this one has a stable sub-compound, which means that a sub-compound of 2 cubes (having one colour in the picture) has a higher symmetry.
It is possible to add one cube, in a similar way as for the classic compound of three cubes. However, it is more beautiful to take another rotation within the rotational freedom, to get a stable sub-compound again.