  We perform a detailed hadron-level study on the sensitivity of Higgs boson
pair production via the $WW^{*}WW^{*}$ channel with the final state $3 \ell 2
j$ + missing $E_T$ at the LHC with the collision energy $\sqrt{S} = 14$ TeV and
a future 100 TeV collider. To avoid the huge background from $pp \to Z W +
\textrm{jets}$ processes, we confine to consider the four lepton patterns:
$e^\pm e^\pm \mu^\mp $ and $\mu^\pm \mu^\pm e^\mp$. We propose a partial
reconstruction method to determine the most reliable combination. After that,
we examine a few crucial observables which can discriminate efficiently signal
and background events, especially we notice that the observable $m_{\rm T2}$ is
very efficient. For the LHC 14 TeV collisions, with an accumulated 3000
fb$^{-1}$ dataset, we find that the sensitivity of this mode can reach up to
1.5 $\sigma$ for the Standard Model and the triple coupling of Higgs boson
$\lambda_3$ in the simplest effective theory can be constrained into the range
[-1, 8] at $95\%$ confidence level; at a 100 TeV collider with the integrated
luminosity 3000 fb$^{-1}$, the sensitivity can reach up to 13 $\sigma$ for the
Standard Model and we find that all values of $\lambda_3$ in the effective
theory can be covered up to 3$\sigma$ even without optimising signals. To
precisely measure the triple coupling of Higgs boson $\lambda_3=1$ of the
Standard Model at a 100 TeV collider, by using the invariant mass of three
leptons which is robust to against the contamination of underlying events and
pileup effects and by performing a $\chi^2$ analysis, we find that it can be
determined into a range [0.8, 1.5] at $95\%$ confidence level.
