They vary by brand, that one looks like it would be 16. A cube has 6 side, but on the storage cube one side is open, so 5 grids for the first cube. Since the second cube shares a side with the first cube, it only has 4 grids. Again the third cube shares a side with the first cube, so 4 more grids. Finally the forth cube shares sides with both the second and the third cube, so it only has 3 grids.
5+4+4+3=16
How many grids you need varies a lot depending on things like are you going to use them for the floors or just the wall? Do you need a top? As well as size.
If you are going really minimal, by using grids only for sides and not flooring or a top, and you make it 2 wide by 3 long by 3 high you need 30 grids. So, 2 boxes as a bare minimum.
Yes, you can use them for bunny proofing. They can be put together, then taken apart and totally reconfigured over and over. They are the handiest things ever.