How can we prove a specific isomorphism between graded Lie algebra and graded universal enveloping algebra?

Let $L$ be a Lie algebra over field of characteristic different from $2$, and let $L_n$ be its descending central series. Therefore, we consider the associated graded Lie algebra $gr^n L =frac{L_n}{L_{n+1}}$. Moreover, let consider that the universal enveloping algebra $U(L)$ which is graded by the augmentation ideal denoted by $I$, that is, $gr U(L)=oplus_{n geq 0} gr^{n} U(L)$, where $gr^{n}U(L)=I^n/I^{n+1}$. How can we show that $I^2/I^{3} cong L_2/L_3 otimes S_{2}(L/L_{2})$, where $S_{2}(L/L_{2})$ is the symmetric algebra of $gr^{2} L$. Thank you for your time.