1.5.13 $\star \star$ Find the largest real number $k$, such that for any positive real numbers $a, b, c$, we have
$$
\begin{aligned}
& \frac{(b-c)^{2}(b+c)}{a}+\frac{(c-a)^{2}(c+a)}{b}+\frac{(a-b)^{2}(a+b)}{c} \\
\geqslant & k\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)
\end{aligned}
$$