  Context. The cusp-core discrepancy is one of the major problems in
astrophysics. It results from comparing the observed mass distribution of
galaxies with the predictions of Cold Dark Matter simulations. The latter
predict a cuspy density profile in the inner parts of galaxies, whereas
observations of dwarf and low surface brightness galaxies show a constant
density core.
  Aims. We want to determine the shape of the dark matter potential in the
nuclear regions of a sample of six nearby irregular dwarf galaxies.
  Methods. In order to quantify the amount of non-circular motions which could
potentially affect a mass decomposition, we first perform a harmonic
decomposition of the HI Hermite velocity fields of all sample galaxies. We then
decompose the HI rotation curves into different mass components by fitting NFW
and pseudo-isothermal halo models to the HI rotation curves using a chi^2
minimisation. We model the minimum-disc, the minimum-disc+gas, and the
maximum-disc cases.
  Results. The non-circular motions are in all cases studied here of the order
of only a few km/s (generally corresponding to less than 25% of the local
rotation velocity), which means that they do not significantly affect the
rotation curves. The observed rotation curves can better be described by the
cored pseudo-isothermal halo than by the NFW halo. The slopes of the dark
matter density profiles confirm this result and are in good agreement with
previous studies. The quality of the fits can often be improved when including
the baryons, which suggests that they contribute significantly to the inner
part of the density profile of dwarf galaxies.
