There is a cohomology theory that resembles Hochschild cohomology and in which both Lie algebra cocycles and quandle cocycles give non-trivial cocycles in the new theory. In this talk, I will discuss a few examples of coalgebras that possess self-distributive products and illustrate the construction of 2-cocycles in this theory. Constructions of 3-cocycles in the cocommutative case will be illustrated.