In this talk, I will use Kuznetsovs description of the derived category of a smooth cubic hypersurface to give a new construction of some stable ACM bundles on cubic threefolds and cubic fourfolds containing a plane. I will also present a wall-crossing phenomenon that allows to relate the compactification of the moduli space of instantons on a cubic threefold with a moduli space of torsion sheaves a non-commutative projective plane. This is a joint work with Emanuele Macr and Paolo Stellari.