  We consider four-dimensional conformal gravity coupled to the U(1) Maxwell
and SU(2) Yang-Mills fields. We study the structure of general black hole
solutions carrying five independent parameters: the mass, the electric U(1) and
magnetic SU(2) charges, the massive spin-2 charge and the thermodynamical
pressure associated with the cosmological constant, which is an integration
constant in conformal gravity. We derive the thermodynamical first law of the
black holes. We obtain some exact solutions including an extremal black hole
with vanishing mass and entropy, but with non-trivial SU(2) Yang-Mills charges.
We derive the remainder of the first law for this special solution. We also
reexamine the colored black holes and derive their first law in
Einstein-Yang-Mills gravity with or without a cosmological constant.
