  A system of equal mixture of $^6Li$ atomic Fermi gas of two hyperfine states
loaded into a cubic three-dimensional optical lattice is studied assuming a
negative scattering length (BCS side of the Feshbach resonance). When the
interaction is attractive, fermionic atoms can pair and form a superfluid. The
dispersion of the phonon-like mode and the speed of sound in the
long-wavelength limit are obtained by solving the Bethe-Salpeter equations for
the collective modes of the attractive Hubbard Hamiltonian.
