In my MSE [question][1], "Conjectured connection between $e$ and $\pi$ in a semidisk", the [answer][2] included

$$\prod_{k=1}^\infty\left[1-\big((k+1)^{1/3}-k^{1/3}\big)^3\right]\approx 0.96454\ldots.$$

Does this infinite product have a closed form?

By "closed form", I mean an expression in terms of known constants. I realize that this is still subjective, but I have found that certain kinds of geometrical constructions yield infinite products with closed forms ([example1][3], [example2][4], [example3][5]). The infinite product in this question also comes from one of these kinds of geometrical constructions, so I wonder if it also has a closed form.


  [1]: https://math.stackexchange.com/q/4915763/398708
  [2]: https://math.stackexchange.com/a/4916881/398708
  [3]: https://math.stackexchange.com/q/4916389/398708
  [4]: https://math.stackexchange.com/q/4337451/398708
  [5]: https://math.stackexchange.com/q/4539739/398708