In his own copy in the Bodleian Library in Oxford (Signature: Savile Gg2)
there is a slip of paper which he inserted, containing a correction of
his former calculations; this was also published by him in vol. 3 of
his Opera (Oxford 1699), p. 695.
I discussed this in a small paper "Das Problem des Prinzen Ruprecht von
der Pfalz", in the journal "Praxis der Mathematik" 10 (1968), 241-246,
where I also considered the same problem for the tetrahedron and the
octahedron.
A discussion of the problem in English (without reference to either
Rupert or Wallis) can be found in the book
"The Cube made Interesting" by Aniela Ehrenfeucht. Oxford and Warsaw 1964
(a translation from a Polish edition), pp. 77-83.
It is possible, though delicate, to build a cardboard model of the
penetrating cubes: the outer one has to be placed such that its contour
has the shape of a regular hexagon, the inner one such that just one square
side is seen.
Have fun!
Christoph J. Scriba