Number of water molecules in a box to simulate liquid water
Generally speaking, you use as many molecules in a simulation as you possibly can. There are a couple of caveats. For instance, if you wish to do a simulation using an expensive method (relative to a classical potential) like DFT, you will need to use fewer molecules. This has the obvious drawback that when you use periodic boundary conditions, each molecule will interact with its own reflections much more than we would like (which is not at all). Nowadays, we can certainly do simulations with more than 32 water molecules using DFT.

Also, there is no reason to just keep using larger and larger numbers because it is known that interactions between molecules in the liquid die off reasonably quickly with distance, so at some point you stop gaining anything by adding more molecules. All of the long range effects can be handled by using periodic boundary conditions, which works very well if each molecule is far enough from its own image that a molecule does not have short-range interactions with itself.

Another consideration is that the number of molecules you use depends a lot on what property you are interested in studying. Conventional wisdom about the number of molecules needed is usually associated with the number of molecules that give converged average energies. If you are interested in something like diffusion coefficients, however, you may need quite a few more molecules before convergence is achieved. I have read that up to 512, or even 768, can be needed to get good diffusion coefficients around room temperature for water.

It is true that sometimes a specific number of molecules is chosen to match a specific density you want to do simulations at. This, however, isn't usually too big of a deal as you can always change your box size to match the density you are trying to achieve.

There is no physical reason that people choose powers of 2 for the number of molecules other than that computational scientists tend to use powers of 2. The number 216 is probably used because some seminal paper used this number and got good results, so people tend to just stick with the trend.