Show that a language with union is not regular by using pumping lemma
If $L$ was regular, so would be $L \cap c^+\Sigma^* = \{c^{2k}w\mid k\geq 1, w\in\{a,b,c\}^* \text{ and }|w|_a = |w|_b\}$.
That means that if you prove that this language is not regular, then $L$ cannot be regular too (that way, we got rid of the union).
Now you can take it from here with pumping lemma, starting from $c^2a^nb^n$!