Greetings to all shiny minds!

I am working on a project that requires computing a uniform distribution of points inside a sphere of radius R.

If we assume that R=1000 and I divide it evenly by 100 then there will be 10 points evenly distributed over the coordinates of a single radius, or 20 points over a single diameter. How can I find how many points exist within the whole sphere?

Is there a formula or an approach that I can use/follow to compute all points that can be evenly distributed in the sphere?

Thank you in advance for your help!