  We use the universal generation of algebraic cycles to relate (stable)
rationality to the integral Hodge conjecture. We show that the Chow group of
1-cycles on a cubic hypersurface is universally generated by lines.
Applications are mainly in cubic hypersurfaces of low dimensions. For example,
we show that if a generic cubic fourfold is stably rational then the
Beauville--Bogomolov form on its variety of lines, viewed as an integral Hodge
class on the self product of its variety of lines, is algebraic. In dimension
$3$ and $5$, we relate stable rationality with the geometry of the associated
intermediate Jacobian.
