Yes, in theory the Cube Puzzle formed by n x n x n small cubes with the Magical Attractors
can be turned like a Rubik's Cube.
The small cubes of a layer which was Twisted / Shifted / Overturned are connected by the force of
Magical Attractors.
Please have a look at these pages below -
http://nytimes.abuzz.com/interaction/s.252689/discussion/e/8.70602/
Magic Attractor - Da Tseng on Feb 28, 2002 (Twisty)
Mechanism? - David on Mar 10, 2002 (Twisty)
Secret - tyler on Mar 10, 2002 (Twisty)