A toy in the form of a hollow cube with clear plastic walls,
small
enough to hold in your hand. Inside of this cube are 7
additional
cubes half as large - leaving one
empty
cube-shaped space within. The inner cubes are metal (or
have
metal inserts) so the player can slide them around
from
outside using a magnet.

The inner cubes are printed with colors, numbers, or
pictures
on
them, and players can scramble and re-arrange them any
way
they like.

Light years of fun for the whole collective. Keeps your little
drones
busy in the back pod - you won't have to listen to them
whining
"are we assimilated yet?" - for the whole trip.

Afterthought - Although I originally pictured it as
an cube of
8
spaces (seven filled, one empty) ... like the prison
in
Dominic
Green's "Smallworld" (link)... you could
have one of any size. The next size up would be a
cube of
27
spaces, 26 filled; then 64/63, and so on until it
become
unwieldy...

The smallest version would be relatively easy as
you can see all of
the pieces, only some of their faces would be
obscured.
The higher-order ones could be fiendishly difficult
as you
can't see any of the inside pieces at all until you
move them
to the perimeter...

To move the "inner" cubes, you would need each cube to
contain a (good, polar) magnet; so you could "push" a whole
row away. There is no other way to move the "inners", at
least beyond 4th order (with 3rd & 4th order, you could
move the gap then "pull" to the boundary).

Yes, I thought of the need to push cubes in any but
the smallest model. Repelling magnets would be a
problem though with so many adjacent pieces.
Maybe the outer casing could be perforated to let
you poke them with a stick.

The original name "Yet Another Cube Toy" just wasn't catchy
enough. New name is fitting as the thing has 7 cubes in
the space of 8 ... with the 8th part empty, like
his head (soul, heart, cojones, whatever)...

xenzag, I hadn't thought of that but you certainly could.
Might have to license it from Scott Adams though, as an 8th
effigy would look a lot like Wally from the Dilbert comic strip.

I envision [MaxwellBuchanan] holding the cube up to the light
and saying something to irritate the cube, just enough though,
to make the afternoon interesting.

Would this be a extremely simple solve? Unlike a two dimensional Sam Loyd puzzle where you can only slide in the x/y, I'm picturing one with a z coordinate where it's an easy process to get a piece in its proper spot by moving it back and behind blocking pieces and then emerging on the other side. Multiply by 6 and you have your cube.

I don't have the maths or visualization skills to answer this properly.

"This must be a thing, immediately" Seriously. I'm surprised
it isn't. I looked online, couldn't find anything like it, thought
one of the first annos would be somebody pointing to one.
Maybe someone with better search skills can find one.

"disliking the name"
Beats calling it "Yet
another cube toy" - got anything better? The name came to
me when I was doing notations for higher order
versions... 27/26, 64/63, and so on.

"would this be extremely simple?"
Yes, I think 8th of 7 is extremely simple. Mindless
entertainment and a fidgeting waste of time, at best ... Oh
wait, did you mean the puzzle? Probably, I haven't done
the math yet either. I think 27 and 64 would be a lot
harder.

It could turn out to be one of those math oddities where it is either so simple it doesn't justify existence, or it's absolutely impossible. I bet Matt Parker would know (or would find out).

Better name? Literally anything else, but start with KDF cube.

Should be trivial to calculate the number of permutations.

7 cubes in 8 spaces... surely there's 8! possible configurations? i.e.40320

A 3x3x3 puzzle has 27 spaces and 26 cubes. 27! possible configurations is 10888869450418352160768000000 which is a bit more of a challenge.

The other thing about 3x3x3 cubes is that the space has limitations on how it can be moved. You could use a push stick to push rows of cubes, but that limits you to having the space in the corners. Using a magnet to drag cubes would let you drag a cube into the corner, shifting the space to the centre of an edge; you could also drag the cube from the centre of a face to the edge to shift the space to the centre of the face. You could then hold the cube in the centre of the opposite face up with the magnet, and turn the whole thing to let the cube in the centre fall to the opposite face, moving the space to the true centre of the whole cube.

For a 4x4x4 cube (64 spaces, 63 cubes, 64! permutations i.e. approximately 1.268869321 E+89), the magnet + gravity trick would allow you to shift the space to any of the 64 spaces. But in a 5x5x5 cube (125 spaces, 124 cubes, 125! permutations, i.e. approx. 1.882677176 E+209), you would not be able to move the space into the exact centre of the cube unless you had a double-strength magnet able to hold two stacked cubes against gravity. And similarly for higher numbers.

"TwistyPuzzles"
Good find, thanks! Now that I know the right
search phrases I see there are lots of good links. One of them
(Varikon2 link) mentions Piet Hein invented one of the earliest
versions. This delights but does not surprise me as I'm already
familiar with some of his other creations.

Could a designed network of magnetic poles be the puzzle? Sliding across a face would take some energy but row pushing same poles or pulling different ones would be the puzzle move to avoid.