  The radiative correction to the Lamb shift of order $\alpha^{2}(Z\alpha)^5m$
induced by the light by light scattering insertion in external photons is
obtained. The new contribution turns out to be equal to
$-0.122(2)\alpha^2(Z\alpha)^5/(\pi n^3)(m_r/m)^3m$. Combining this contribution
with our previous results we obtain the complete correction of order
$\alpha^{2}(Z\alpha)^5m$ induced by all diagrams with closed electron loops.
This correction is $37.3(1)$ kHz and $4.67(1)$ kHz for the $1S$- and
$2S$-states in hydrogen, respectively.
