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In all available papers, on power integral bases of pure octic number fields$K$, generated by a root $\alpha$ of a monic irreducible polynomial$f(x)=x^8-m\in\mathbf Z[x]$, it was assumed that $m\neq \pm 1$ is square free.In this paper, we investigate the monogenity of any pure octic number field,without the condition that $m$ is square free. We start by calculating anintegral basis of $\mathbf Z_K$, the ring of integers of $K$. In particular, wecharacterize when $\mathbf Z_K=\mathbf Z[\alpha]$. We give sufficientconditions on $m$, which guarantee that $K$ is not monogenic. We finish thepaper by investigating the case when $m=a^u$, $u\in\{1,3,5,7\}$ and $a\neq \mp1$ is a square free rational integer.

On integral bases and monogenity of pure octic number fields with non-square free parameters