  The $h$-polynomial of the barycentric subdivision of any $n$-dimensional
cubical complex with nonnegative cubical $h$-vector is shown to have only real
roots and to be interlaced by the Eulerian polynomial of type $B_n$. This
result applies to barycentric subdivisions of shellable cubical complexes and,
in particular, to barycentric subdivisions of cubical convex polytopes and
answers affirmatively a question of Brenti, Mohammadi and Welker.
