  We performed a series of high-resolution $N$-body simulations to examine
whether dark matter candidates in the form of primordial black holes (PBHs) can
solve the cusp-core problem in low-mass dwarf galaxies. If some fraction of the
dark matter in low-mass dwarf galaxies consists of PBHs and the rest is cold
dark matter, dynamical heating of the cold dark matter by the PBHs induces a
cusp-to-core transition in the total dark matter profile. The mechanism works
for PBHs in the 25-100 M$_{\sun}$ mass window, consistent with the LIGO
detections, but requires a lower limit on the PBH mass fraction of 1$\%$ of the
total dwarf galaxy dark matter content. The cusp-to-core transition time-scale
is between 1 and 8 Gyr. This time-scale is also a constant multiple of the
relaxation time between cold dark matter particles and PBHs, which depends on
the mass, the mass fraction and the scale radius of the initial density profile
of PBHs. We conclude that dark matter cores occur naturally in halos comprised
of cold dark matter and PBHs, without the need to invoke baryonic processes.
