  We give a complete characterization of the parity of $b_8(n)$, the number of
$8$-regular partitions of $n$. Namely, we prove that $b_8(n)$ is odd or even
depending on whether or not we have the factorisation $24n+7=p^{4a+1}m^2$, for
some prime $p\nmid m$ and $a\ge 0$.
