  We classify central extensions of a reductive group $G$ by $\mathcal{K}_3$
and $B\mathcal{K}_3$, the sheaf of third Quillen $K$-theory groups and its
classifying stack. These turn out to be parametrized by the group of
Weyl-invariant quadratic forms on the cocharacter lattice valued in $k^\times$
and the group of integral Weyl-invariant cubic forms on the cocharacter lattice
respectively.
