I know that buying a chocolate cake mix would be the easiest, but there is a white cake mix whose flavor I like...
A small amount will be fine, but if you try to add enough to make it significantly chocolate flavored, you'll throw off both the wet/dry ratio and the acid chemistry of the mix, and probably end up with an unsatisfactory cake.
What may be easier is to get unsweetened chocolate (Baker's is the most common brand around here). Melt it (I do it in the microwave) and stir it into the batter once it's made. Minor stirring will make it marbled, and major stirring will give you chocolate cake. This can solve the problem of throwing off the wet/dry ratio Michael mentioned.
In a scratch white cake recipe, you could replace part of the flour with an equal amount of unsweetened cocoa. However, that's not possible with a cake mix, which already has the sugar and flour mixed together.
I would recommend either adding a small amount of melted unsweetened chocolate (no more than 2oz) or you could add chocolate extract.
Yes. Use a little if color's the only thing you care about. If you want more chocolate taste, you may require additional tricks.
For the added chocolate, put the Hershey's powdered chocolate in the dry mix, mix well; go from there. You got your chocolate. No problem
consider adding hot chocolat mix instead of coca, and add some extra liquid, if you add more than 1/4 c total ingredients you might need to adjust the spices and levening (powder/soda)