  We have recently demonstrated the laser cooling of a single $^{40}$Ca$^+$ ion
to the motional ground state in a Penning trap using the resolved-sideband
cooling technique on the electric quadrupole transition S$_{1/2}
\leftrightarrow$ D$_{5/2}$. Here we report on the extension of this technique
to small ion Coulomb crystals made of two or three $^{40}$Ca$^+$ ions.
Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime
on a two-ion string along the magnetic field axis as well as on two- and
three-ion planar crystals. Complex sideband cooling sequences are required in
order to cool both axial degrees of freedom simultaneously. We measure a mean
excitation after cooling of $\bar n_\text{COM}=0.30(4)$ for the centre of mass
mode and $\bar n_\text{B}=0.07(3)$ for the breathing mode of the two-ion string
with corresponding heating rates of 11(2) s$^{-1}$ and 1(1) s$^{-1}$ at a trap
frequency of 162 kHz. The ground state occupation of the axial modes is above
75% for the two-ion planar crystal and the associated heating rates 0.8(5)
s$^{-1}$ at a trap frequency of 355 kHz.
