  We exhibit explicit examples of very general special cubic fourfolds with
discriminant $d$ admitting an associated (twisted) K3 surface, which have
non-isomorphic Fourier-Mukai partners. In particular, in the untwisted setting,
we show that the number of Fourier-Mukai partners for a very general special
cubic fourfold with discriminant $d$ and having an associated K3 surface, is
equal to the number $m$ of Fourier-Mukai partners of its associated K3 surface,
if $d \equiv 2 (\text{mod}\,6)$; else, if $d \equiv 0 (\text{mod}\,6)$, the
cubic fourfold has $\lceil m/2 \rceil$ Fourier-Mukai partners.
