How can I minimize the function in the form of 1/(x^3-1), with x>1?

4

You can do
minimize(pow_p(x,-3)+pow_p(y,-3))

As for 1/(x^3-1) for x > 1, it appears that none of the forum readers know how to formulate that in CVX, despite its convexity. Therefore, it is a candidate for @Erling’s challenge. https://twitter.com/J_P_Vielma/status/1014513695605608448

Edit: I stand corrected on the preceding paragraph in light of @Michal_Adamaszek’s post below.