  We study the behavior of the degree of the colored Jones polynomial and the
boundary slopes of knots under the operation of cabling. We show that, under
certain hypothesis on this degree, if a knot $K$ satisfies the Slope Conjecture
then a $(p, q)$-cable of $K$ satisfies the conjecture, provided that $p/q$ is
not a Jones slope of $K$. As an application we prove the Slope Conjecture for
iterated cables of adequate knots and for iterated torus knots. Furthermore we
show that, for these knots, the degree of the colored Jones polynomial also
determines the topology of a surface that satisfies the Slope Conjecture. We
also state a conjecture suggesting a topological interpretation of the linear
terms of the degree of the colored Jones polynomial (Conjecture \ref{conj}),
and we prove it for the following classes of knots:iterated torus knots and
iterated cables of adequate knots, iterated cables of several non-alternating
knots with up to nine crossings, pretzel knots of type $(-2, 3, p)$ and their
cables, and two-fusion knots.
