  The aim of this paper is to investigate the algebraic structure that appears
on $|3|-$gradings $\mathfrak{n}=\mathfrak{n}_{-3}\oplus \cdots \oplus
\mathfrak{n}_3$ of a complex simple Lie algebra $\mathfrak{n}$. In particular,
we completely determine the possible reductive algebras $\mathfrak{n}_0$ and
prove that the only free nilpotent Lie algebra of step 3 that appears as the
negative part $\mathfrak{n}_{-3}\oplus\mathfrak{n}_{-2}\oplus\mathfrak{n}_{-1}$
of a grading is the usual $|3|-$grading of the exceptional Lie algebra
$\mathfrak{g}_2$.
