Many of quasitoric manifolds over cubes can be regarded as fiber bundles, whose fibers and base spaces are also quasitoric manifolds over cubes (for example, a Bott manifold is an iterated $\mathbb{C}P^1$-bundle over $\mathbb{C}P^1$). I'd like to talk about some classification results of such manifolds, mainly, the cohomological rigidity of iterated ($\mathbb{C}P^2\sharp\mathbb{C}P^2$)-bundles over $\mathbb{C}P^2\sharp\mathbb{C}P^2$.