Make yourself familiar with the concept of elastic stability. The elastic energy due to every possible strain of a stable crystal structure must be positive. For cubic symmetry, this implies (I think) C11 >0, C11-C12 > 0 and C44 > 0. If this not the case under some boundary conditions, this is a sign that a structure having a broken symmetry has a lower energy than the cubic structure. Apart from elastic stability, also consider the possibility of dynamic instability.

you can simulation for this