Given a cube:

And a point anywhere inside that cube.

Could that point be reinterpreted given any kind of deformation applied to the cube?

I.e., where would that point be inside the deformed cube?

The cube could be deformed in any way, and we only know the location of the vertices.

Likewise, given a point in relation to the distorted cube, could we find where that point is in relation to the undistorted cube?

The vertices of the cube are indexed and stay the same between the undistorted and the distorted cube.