  We investigate the formation and condensation of fermion pairs in cold atom
quantum simulators for extended Hubbard models (UV models) with body center
cubic (BCC) optical lattices, predicting small and light pairs with
Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair
mass, radius, and binding conditions are calculated, and then used to compute
transition temperatures. We predict that: (a) local pairs can form in BCC
optical lattices; (b) for particular cases where the onsite $U$ and intersite V
are attractive with similar size, the pairs are both small and light; and (c)
that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms
in blue (red) BCC optical lattices. Beyond the application to pairs on BCC
optical lattices, we expect our results to be relevant to strong-coupling BCC
superconductors.
