  We investigate formation and condensation of fermion pairs in cold-atom
quantum simulators for extended Hubbard models ($UV$ models) with
body-centered-cubic (BCC) optical lattices in the dilute limit, predicting
small and light pairs. Pair mass, radius, and binding conditions are
calculated, and used to compute transition temperatures. We predict that: (a)
local pairs form in BCC optical lattices and binding energies can be large; (b)
for particular cases where onsite $U$ and intersite $V$ are attractive with
similar size, pairs are both small and light; and (c) pairs of $^6$Li atoms
Bose--Einstein condense at temperatures of around 10 nK.
