To solve for \( b \) in the expression \( b = \sqrt[3]{89}^3 \), we can simplify it as follows:
- Recognize that taking the cube root and then cubing a number will cancel each other out. Thus: \[ b = \left(\sqrt[3]{89}\right)^3 = 89 \]
So, the final answer is: \[ b = 89 \]