Gaining information about the shape of the Higgs potential is one of the main goals of particle physics for the coming years. The trilinear Higgs self-interactions can directly be probed via Higgs pair production, which at the LHC happens dominantly through gluon fusion. In models with extended Higgs sectors the trilinear self-coupling of the detected Higgs boson can strongly deviate from the prediction of the Standard Model (SM) due to large loop corrections even in scenarios where all couplings to gauge bosons and fermions are very close to their SM values. Furthermore, triple Higgs couplings involving additional Higgs bosons can have an important impact on the pair production process of the SM-like Higgs boson via the resonant contribution of the heavy Higgs. We study the phenomenological implications for Higgs pair production in the framework of the Two Higgs Doublet Model (THDM). We analyze the potential sensitivity to both, the SM-like trilinear Higgs self-coupling and the beyond-the-SM triple Higgs coupling involving a resonantly produced CP-even Higgs. In particular, we focus on the theoretical predictions of two observable quantities: the total Higgs pair production cross section and the invariant mass distribution of the two Higgs bosons in the final state. We show that the inclusion of loop corrections to the trilinear Higgs couplings as well as the resonant heavy Higgs contribution are crucial in this context.