Is there a closed-form expression for $\prod_{n=1}^{\infty}(1-\frac{x}{n^3})$? I would like to ask if for $|x|<1$, we can express the product $\prod_{n=1}^{\infty}(1-\frac{x}{n^3})$ as a function $f(x)$. I tried to use Weierstrass factorization theorem, but without much success.
I would really appreciate a reference or a solution.

Comment:
The bound of this product can be found usig Weierstrassn inequality:
If $a_1, a_2, a_3, \ldots,a_n$ are real positive integers less than unity, and:
$S_n=(a_1+a_2+a_3+ \cdots+a_n)<1$
then:
$1-S_n<(1-a_1)(1-a_2)(1-a_3)  \cdots (1-a_n)<\frac 1 {1+S_n}$
Where we can let:
$a_n=\frac x {n^3}$
