define a box packing as gap-less if

• all inner boxes have disjoint interior
• the sum of volumes of the iiner box equals that of the outer box
• the sum of the extents of the inner boxes in each principal direction equals that of the outer box

define a box paxking as stable if

• for every hyperplane with a point inside the outer box there is an inner box with inner points to both sides of that hyperplane.

Questions:

• for which $k$, depending on dimension $n$ of the boxes do stable gap-less packings of boxes with boxes exist?
• how can such packings be found, given $k$ and $n$?

In $2{-}d$ there are many examples from squaring the square which is a very special case of this question for $n=2$; this question allows boxes of equal size and arbitrary extents in each principal direction.