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Ludwik-
I spare the readers a repeat of your posting.
Have you forgotten that the net force on the system is zero,
since it is neutral? The center of mass therefore does not move.
The nucleus at the center is thousands of times heavier than the
electronic cloud, so the nucleus also does not, to a good approximation,
move; only the cloud does. I will look at the rest of your calculation
with this in mind, but cubes are less tractable than spheres for
simple calculations.