  In this paper, a large family of topological black hole solutions of
dimensionally continued gravity are derived. The action of Lovelock gravity is
coupled to the exponential electrodynamics and the equations of motion are
solved in the presence of a pure magnetic source. We work out the metric
functions in terms of the parameter $\beta$ of exponential electrodynamics, and
magnetic charge. Further, we couple Lovelock gravity to power-Yang-Mills theory
and construct black holes, in diverse dimensions, having Yang-Mills magnetic
charge. We also discuss the asymptotic bahaviour of metric functions and
curvature invariants at the origin for both the models. The thermodynamics of
resulting magnetized black hole solutions in the framework of two different
models is also studied. The thermodynamical quantities like Hawking
temperature, entropy and specific heat capacity at constant charge are found
and we show that the resulting quantities satisfy the first law of black hole
thermodynamics. We also study the magnetized hairy black holes of dimensionally
continued gravity.
