I made essentially the same assertion some months back (about the 5x5x5
being the last "interesting" cube), and someone pointed out that there
is a position in even order cubes which has no parallel in odd order cubes--
that where all the corner cubies are correct, but all the edge cubies on
the top layer are wrong. The presence of the fixed center cubie makes it
clear that the edge cubies are really all wrong.
Boy it's great to get cube mail again.