I think its tricky if you want to have the same set of colours in each box, if you want to randomise the 9 colours across all boxes then you could approach it with a slightly different set up, I dont have redshift and only R18 so there may be a node solution out there but in mograph I would do it like this, first separate the box out into its own duplicate cloner.
Then instead of cloning the spheres into a box clone an object, I like to use a single poly plane. so instead of 81 spheres you have 81 polys created in the two cloners, now drop that cloner of planes into a connect object to make it one piece as far as mograph is concerned.
Now you can clone your spheres onto the connect object and also effect all of them with a single random effector, Im using multi shader here to get the same 9 colors.
Deck
random col test.c4d