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We show that under a generic condition, the quadratic Gaudin Hamiltoniansassociated to $\mathfrak{gl}(p+m|q+n)$ are diagonalizable on any singularweight space in any tensor product of unitarizable highest weight$\mathfrak{gl}(p+m|q+n)$-modules. Moreover, every joint eigenbasis of theHamiltonians can be obtained from some joint eigenbasis of the quadratic GaudinHamiltonians for the general linear Lie algebra $\mathfrak{gl}(r+k)$ on thecorresponding singular weight space in the tensor product of somefinite-dimensional irreducible $\mathfrak{gl}(r+ k)$-modules for $r$ and $k$sufficiently large. After specializing to $p=q=0$, we show that similar resultshold as well for the cubic Gaudin Hamiltonians associated to$\mathfrak{gl}(m|n)$.  We also relate the set of singular solutions of the (super)Knizhnik-Zamolodchikov equations for $\mathfrak{gl}(p+m|q+n)$ to the set ofsingular solutions of the Knizhnik-Zamolodchikov equations for$\mathfrak{gl}(r+k)$ for $r$ and $k$ sufficiently large.

Quadratic and cubic Gaudin Hamiltonians and super Knizhnik-Zamolodchikov equations for general linear Lie superalgebras