  In this paper we compute the cohomology of moduli space of cubic fourfolds
with ADE type singularities relying on Kirwan's blowup and Laza's GIT
construction. More precisely, we obtain the Betti numbers of Kirwan's
resolution of the moduli space. Furthermore, by applying decomposition theorem
we obtain the Betti numbers of the intersection cohomology of Baily-Borel
compactification of the moduli space.
