  The finite lattice method of series expansion has been used to extend
low-temperature series for the partition function, order parameter and
susceptibility of the $3$-state Potts model on the simple cubic lattice to
order $z^{43}$ and the high-temperature expansion of the partition function to
order $v^{21}$. We use the numerical data to show that the transition is
first-order, and estimate the latent heat, the discontinuity in the
magnetisation, and a number of other critical parameters.
