Meshes use triangles. If you are looking for faces, that has to be defined somehow for the mesh, as it’s not clear what a face is for a generic mesh.
Assuming we can associate a triangle with a face somehow, then a brute force way is to intersect the triangles of the small cube against the triangles of the big cube. If they intersect, then remove it along with associated triangles of the same face from the small cube. If not, then you keep it.
I don’t see any code in Babylon.js that is available to call directly that gives you this Boolean operation of whether two triangles intersect. I found one based on three.js here that maybe can be ported.