We use molecular dynamics simulations to study the stabilization of the hexameric, cagelike silicate with double three-ring structure in aqueous and methanolic solutions. We find that in purely aqueous environments its stabilization requires the presence of both tetramethylammonium and tetraethylammonium (TEA) cations and involves the formation of a stable TMA layer which leads to a water-silicate heteronetwork clathrate. We also find that TEA alone can facilely stabilize the hexamer when methanol cosolvent is added, in accordance with experiment. The mechanism of this stabilization, however, differs from that in purely aqueous environments. Because of the unique properties of water-methanol mixtures, the organosilicate complex does not participate in heteronetwork clathrates but resides in a large solvent cavity; that is, it is forced out of true solution.