Exponential and logarithm Series

Let $\large\sqrt[3]{x}=\dfrac{k}{y^2} \color{#3D99F6}{ \text{(for some constant k)}}$ Plug in $x=8$ $\text{and}$ $y=3 \rightarrow$ $\large\implies k=9\cdot2=18$ Now plug in $y=\dfrac32 \text{in the main equation to get} \rightarrow$ $\large\implies x=\left(\dfrac{4k}9 \right)^3$ now plug in the value of k obtained above to get $\rightarrow$ $\large\implies x=8^3=\color{#D61F06}{\boxed{512}}$