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.