  In this paper, we shall prove the equality \[
\zeta(3,\{2\}^{n},1,2)=\zeta(\{2\}^{n+3})+2\zeta(3,3,\{2\}^{n}) \] conjectured
by Hoffman using certain identities among iterated integrals on
$\mathbb{P}^{1}\setminus\{0,1,\infty,z\}$.
