  The $\ell$-adic Galois polylogarithm is an arithmetic function on an absolute
Galois group with values in $\ell$-adic numbers, which arises from Galois
actions on $\ell$-adic \'etale paths on ${\mathbb P}^1 \backslash
\{0,1,\infty\}$. In the present paper, we discuss a relationship between
$\ell$-adic Galois polylogarithms and triple $\ell$-th power residue symbols in
some special cases studied by a work of Hirano-Morishita. We show that a
functional equation of $\ell$-adic Galois polylogarithms by Nakamura-Wojtkowiak
implies a reciprocity law of triple $\ell$-th power residue symbols.
