Cocycles of nilpotent quotients of free groups

We focus on the cohomology of the $k$-th nilpotent quotient of the free group, $F\mathrm{/}{F}_k$. This paper describes all the group 2-, 3-cocycles in terms of Massey products, and gives expressions for some of the 3-cocycles. We also give simple proofs of some of the results on Milnor invariants and the Johnson-Morita homomorphisms.