Can I substitute whole eggs for egg whites in cake mix?
If you truly desire a white cake, you don't want to make this substitution.

The reason the white cake mix directs you to add egg whites only is to to avoid the yellow color from the yolks, which will tint your cake yellowish.  

Cake mixes are highly engineered wonders, and are very tolerant of almost everything a home cook can do to go wrong within reason.  Still, substituting in the yolks increases the amount of fat&mdash;and more importantly, the emulsifier lecithin, and so will change the texture of the outcome.  This will probably not be bad, but still will not be the optimal result from your mix.