We present Local Density Functional calculations of the structural and electronic properties of halosodalite systems in which the Na+ cations are progressively exchanged by Cu+. The calculated lattice constant decreases with increasing Cu loading up to about two Cu/cage, while it is approximately independent of Cu content at higher loadings, in qualitative agreement with experimental observations for silver-exchanged sodalites. The reduction of the lattice parameter is accompanied by the formation of partially covalent Cu-X bonds (X=Cl, Br). The length of these bonds increases with increasing the number of Cu ions per cage, resulting in a simultaneous reduction of Cu-framework distances. For fully exchanged sodalites, the competition between Cu-X and Cu-framework interactions leads to a splitting of the enclosed Cu4X3+ aggregates in fragments. In the electronic density of states, Cu 3d states give rise to a narrow band above the top of the valence band of natural sodalite. Thus the band gap is strongly reduced w.r.t. that of natural sodalite, consistent with experiments for silver-exchanged sodalites. This reduction of the gap is largely independent of the Cu content, i.e., it already occurs at low Cu loading.