In my MSE question, "Conjectured connection between $e$ and $\pi$ in a semidisk", the answer turned out to be

$$\prod\limits_{k=1}^\infty\left[1-\big((k+1)^{1/3}-k^{1/3}\big)^3\right]\approx 1.56813\dots$$

Does this infinite product have a closed form?