  Despite the discovery of a Higgs boson h(125GeV) at the LHC Run-1, its
self-interaction has fully evaded direct experimental probe so far. Such
self-interaction is vital for electroweak symmetry breaking, vacuum stability
and electroweak phase transition, and Higgs inflation. It is a most likely
place to encode new physics beyond the standard model. We parametrize such new
physics by model-independent dimension-6 effective operators, and study their
tests via Higgs pair production at hadron colliders. We analyze three major
di-Higgs production channels at parton level, and compare the
parameter-dependence of total cross sections and kinematic distributions at the
LHC(14TeV) and pp(100TeV) hadron collider. We further perform full simulations
for the di-Higgs production channel $gg\to hh \to b\bar{b}\gamma\gamma$ and its
backgrounds at the pp(100TeV) hadron collider. We construct four kinds of
benchmark points, and study the sensitivities to probing different regions of
the parameter space of cubic Higgs interactions. We find that for one-parameter
analysis and with a 3/ab (30/ab) integrated luminosity, the $gg\to hh \to
b\bar{b}\gamma\gamma$ channel can measure the SM cubic Higgs coupling and the
derivative cubic Higgs coupling to an accuracy of about 13% (4.2%) and 5%
(1.6%), respectively.
