The "stuffed" fullerenes (a fullerene with an atom or more inside the cage) are called Endohedral fullerenes
(Wikipedia article). They are generally produced by trapping the caged atom inside, before the cage is completed (during synthesis of the fullerene), but they have also been made by chemically opening the cage (breaking some of the bonds), inserting the atom inside, and reclosing the cage.
The interest, at least in the carbon systems, is to change the properties of the fullerene.