We focus on the cohomology of the $k$-th nilpotent quotient of a free group. We describe all the group 2-, 3-cocycles in terms of the Massey product and give expressions for some of the 3-cocycles. We also give simple proofs of some of the results on the Milnor invariant and Johnson–Morita homomorphisms.
"Cocycles of nilpotent quotients of free groups." J. Math. Soc. Japan 72 (1) 171 - 184, January, 2020. https://doi.org/10.2969/jmsj/79997999