  In arXiv:1204.2810 Agol proved the Virtual Haken and Virtual Fibering
Conjectures by confirming a conjecture of Wise: Every cubulated hyperbolic
group is virtually special. We extend this result to cocompactly cubulated
relatively hyperbolic groups with minimal assumptions on the parabolic
subgroups. Our proof proceeds by first recubulating to obtain an improper
action with controlled stabilizers (a weakly relatively geometric action), and
then Dehn filling to obtain many cubulated hyperbolic quotients. We apply our
results to prove the Relative Cannon Conjecture for certain cubulated or
partially cubulated relatively hyperbolic groups.
  One of our main results (Theorem A) recovers via different methods a theorem
of Oreg\'on-Reyes (arXiv:2003.12702).
