Write an equation describing the relationship of the given variables. $y$ varies inversely as the cube root of $x$ and when $x=8, y=2$.

Step 1 ：Write an equation describing the relationship of the given variables: $y = k * \frac{1}{\sqrt[3]{x}}$

Step 2 ：Use the given values $x=8$ and $y=2$ to find the value of $k$: $2 = k * \frac{1}{\sqrt[3]{8}}$

Step 3 ：Solve for $k$: $k = 4$

Step 4 ：Write the final equation with the value of $k$: \(\boxed{y = 4 * \frac{1}{\sqrt[3]{x}}}\)