  We combine the detailed Star Formation Histories of the Fornax and Sculptor
dwarf Spheroidals with the Mass Assembly History of their dark matter (DM) halo
progenitors to estimate if the energy deposited by Supernova type II (SNeII) is
sufficient to create a substantial DM core. Assuming the efficiency of energy
injection of the SNeII into DM particles is $\epsilon_{\rm gc}=0.05$, we find
that a single early episode, $z \gtrsim z_{\rm infall}$, that combines the
energy of all SNeII due to explode over 0.5 Gyr, is sufficient to create a core
of several hundred parsecs in both Sculptor and Fornax. Therefore, our results
suggest that it is energetically plausible to form cores in Cold Dark Matter
(CDM) halos via early episodic gas outflows triggered by SNeII. Furthermore,
based on CDM merger rates and phase-space density considerations, we argue that
the probability of a subsequent complete regeneration of the cusp is small for
a substantial fraction of dwarf-size haloes.
