Answer
$x=2$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{8}x=\frac{1}{3}$ is equivalent to $8^{\frac{1}{3}}=x$.
Therefore, $x=2$, because $8^{\frac{1}{3}}=\sqrt[3] 8=2$.