The ElasticConstants analysis object has the default option enable_symmetry=True, which means that only linearly independent elastic constants are calculated. For an FCC lattice with space group 225, only 3 elastic constants are therefore calculated. Example: (script attached)
+------------------------------------------------------------------------------+
| Calculating elastic constants for the given bulk configuration |
+------------------------------------------------------------------------------+
| Detected space group number: 225 |
| Detected lattice symmetry: Cubic |
| This lattice symmetry has 3 independent elastic constants: |
| C11 C12 C44 |
+------------------------------------------------------------------------------+
As long as the configuration that you give as input for ElasticConstants analysis has space group 225, only those 3 elastic constants will be calculated. If the input lattice does not reconstruct when subjected to small strains, I think your calculation should be ok.