That 25.95% assumes you've carefully packed each layer, arranging them perfectly for maximum efficiency. For "random" packing, that number is closer to 35%.
So, closer to 7,000 balls, practically speaking.
Yeah, I didn't really feel like trying to get too into it so I figured a cube but went slightly smaller on all sides to account for balls nestling into the crooks between adjacent balls.
I mean, that's how most of my "calculations" go anyway. Estimate, estimate, estimate! (Then round up to the safe side) :)