# Homotopy pullback of a homotopy pushout is a homotopy pushout

Let's assume that we have a cube of spaces such that everything commutes up to homotopy. The following holds:
- The right square is a homotopy pushout and
- all the squares in the middle are homotopy pullbacks.
I was told that (in Top) the left square is also a homotopy pushout then. Do you know any source where this is stated? (Or: is this actually true?)