Hume (of whom I have only read occasional excerpts) seems to be full of it. Full of skepticism and empiricism and attempts at refutations of (his caricature of) theism, I mean. The famous Hume's fork is famous for the reason that it seems as effective as the Epicurean paradox against theism.

Kant, on the other hand, only dealt with the ontological argument, and only with the Cartesian version of it. Kant thought - given his own metaphysics - that God cannot be proven, but he equally solidly thought that God cannot be disproven. This because God is noumenal, and noumena are like that, empirically unprovable. But noumena are not non-existent.