  We have computed the contributions of the quartic Casimir invariants to the
four-loop anomalous dimensions of twist-2 spin-N operators at N =< 16. The
results provide new information on the structure of the
next-to-next-to-next-to-leading order (N^3LO) splitting functions P_{ik}^(3)(x)
for the evolution of parton distributions, and facilitate approximate
expressions which include the quartic-Casimir contributions to the (light-like)
gluon cusp anomalous dimension. These quantities turn out to be closely
related, by a generalization of the lower-order `Casimir scaling', to the
corresponding quark results. Using these findings, we present an approximate
result for the four-loop gluon cusp anomalous dimension in QCD which is
sufficient for phenomenological applications.
