Yes. If we start from any two particles of this system, the center of mass (say A) of these two particles will lie on the line joining them. This line will be fully inside the cube. Next, these two particles can be replaced with their total mass at this center of mass A. Now the center of mass of third particle and previous two particles will lie on the line joining the third particle and A, Say this center of mass as B. Again this line joining A and third particle is fully inside the cube, so B is also inside the cube. The total mass of three particles can be assumed to be at B. In this way we can show that the center of mass of all the particles of a system that **** in a cube is necessarily in the cube.
