In this paper, routing properties of cube-based optoelectronic OTIS networks are explored. We show emulations of various cubical network topologies on their OTIS augmented variants, including the n-D grid networks, shuffle-exchange, and de Brujin networks. An analytical performance model for OTIS-cube networks is proposed. The model is validated by means of comparison with rigorously obtained simulation results. Using this model, the performance characteristics of the OTIS-hypercube network are evaluated in view of a number of different constraints. Moreover, we compare the performance characteristics of the OTIS-hypercube with that of equivalent fully-electronic networks under various implementation constraints.