Write $\sum\limits_{n=0}^\infty e^{-xn^3}$ in the form $\sum\limits_{n=-\infty}^\infty a_nx^n$

In order for $\varsigma(x)$ to have a Laurent series in a deleted neighbourhood of $0$, $f$ must be analytic in that deleted neighbourhood. But I'm pretty sure the function $\sum_n z^{n^3} = \varsigma(-\log(z))$ has a natural boundary on $|z|=1$. Therefore no such Laurent series is possible.

EDIT: The Fabry gap theorem says that if $\sum_n \alpha_n z^{p_n}$ has radius of convergence $1$, where $p_n$ is an increasing sequence of integers with $p_n/n \to \infty$, then the unit circle is a natural boundary for this series.