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We investigate formation and condensation of fermion pairs in cold-atomquantum simulators for extended Hubbard models ($UV$ models) withbody-centered-cubic (BCC) optical lattices in the dilute limit, predictingsmall and light pairs. Pair mass, radius, and binding conditions arecalculated, 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 withsimilar size, pairs are both small and light; and (c) pairs of $^6$Li atomsBose--Einstein condense at temperatures of around 10 nK.

Fermion pairing in body-centered-cubic quantum simulators of extended Hubbard models