Hypercubes were used by Time Lords to send telepathic messages across great distances of Space and Time. (TV: The War Games, The Doctor's Wife)
According to Alice, they could travel through Space, Time, Dreams and Realities, thus making them even more polyvalent than TARDISes — although their usefulness as vessels for travel of individuals, as opposed to ideas, was lessened by the fact that one couldn't escape from within a Hypercube on one's own. (WC: House Call)