Yes, it is necessary that the center of mass of such a system of particles lie inside the cube.

Explanation:

The center of mass of a system of particles is the weighted average position where we can assume the whole mass of the

system is concentrated. Consider for example, a 2-particle system. One particle has a mass m₁ and other particle has a mass m₂. Let . The centre of mass of this system will be located between the line joining the two particles and it will be closer to the particle with mass m₁.

Similarly, in this case, even if we assume that the heaviest particle is located near the edge of the cube, then also the center of mass will be present in between the line joining this particle and any other particle inside the cube. So extending in this fashion, we can say that the center of mass in this case is inside the cube.