Well, at least, I managed to take all cubes off the
core. I studied the patent, and found the courage to
try to take the cube apart risking to break it.
In fact, each cube is actually a put-on cap that is
attached to the cube's core. A cube only has three
walls, and on the internal side of two of them there
are two slides that are slid into grooves that stretch
out of the core for each of eight cubes. Now, there is
also a spear/harpoon-like lock tongue (I don't know the
real name for this thing) that locks to the core when
the cube is pushed on the slides all way down to the
core.

So, to take a cube off, you turn a side of the puzzle
45 degrees and see an empty inside of a cube. If you
take a good look inside at this point, you'll see the
grooves, and you will see the end of the lock tongue.
All you need to do is to pull it up with a small tool
like a small screwdriver, and while holding it up, push
the cube away from the core. That can take some effort
as it may not come off very easy. I was really afraid
that I might break it, but in the end, after I took it
off, I could see that these grooves, tongues, and the
lock are in fact quite sturdy.

So, you can try it for ourself. If lots of people want
to see it all in photos, I can try to take some on a
weekend. But really, all that is in the picture of the
patent.