  We study structures of embedded projective manifolds swept out by cubic
varieties. We show if an embedded projective manifold is swept out by
high-dimensional smooth cubic hypersurfaces, then it admits an extremal
contraction which is a linear projective bundle or a cubic fibration. As an
application, we give a characterization of smooth cubic hypersurfaces. We also
classify embedded projective manifolds of dimension at most five swept out by
copies of the Segre threefold P^1\timesP^2. In the course of the proof, we
classify projective manifolds of dimension five swept out by planes.
