Misael,

Even in two dimensions and for very simple containing figures such as squares, there is no satisfactory general solution to the question of how many balls of a given size can be packed into a given region.

Reasonable approximations can often be obtained by computer programs that use trial and error. In my experience it is probably best to solve (one of) the dual problem(s) of how large R can be while fitting N balls of radius R into your region. This works better because the radius can be changed continuously while the number cannot be.

You could start with a genetic algorithm or something similar. If you can find a variation that allows you to make use of proximity data this might pay off in drastically increased speed.

But you'll have to experiment. All I can tell you is that you are probably in genuinely new territory, and if you find any result that has a good motivation your results might be publishable.

Good Hunting!
RD