  An L-space link is a link in $S^3$ on which all sufficiently large integral
surgeries are L-spaces. We prove that for m, n relatively prime, the
r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an
L-space knot and $n/m \geq 2g(K)-1$. We also compute HFL-minus and HFL-hat of
an L-space cable link in terms of its Alexander polynomial. As an application,
we confirm a conjecture of Licata regarding the structure of HFL-hat for (n,n)
torus links.
