We present a local density functional study of Cd4S and Cd4S4 clusters inside sodalite cages of different compositions (Al:Si ratios). The composition of the framework determines the cluster --> cage charge transfer and strongly affects the atomic structure of the inclusion. The energy gap and the character of the highest occupied (HOMO) and lowest unoccupied (LUMO) electronic states depend on the size and stoichiometry of the included clusters, as well as on the overall stoichiometry of the composite. The calculated gap for Cd4S inclusions in aluminosilicate and aluminate sodalite (at half and full packing respectively) is similar to 2.5 eV (i.e., about twice the calculated gap of bulk CdS), while for Cd4S4 in aluminosilicate and pure silica sodalite (at half packing) it is 1.7-1.9 eV (i.e., about 1.5 times the gap of bulk CdS). Our results indicate that simple confinement arguments are usually insufficient to predict the behavior of semiconductor-zeolite composites.