Can you substitute egg whites for whole eggs in a box of yellow cake mix to make the cake white? 

I'd guess that yellow cake mix has food coloring in ti, so I would think that you can't do that. Check the label to see if there are any colors or if they list beta carotene as an ingredient.

Yeah what she ^^^ said.  No it won't turn white because the actual color of the mix is yellow to begin with.  Taste wise it will come close but will never be white in color. 

You can try adding a few drops of violet color and a little white food to the mixture, along with using egg whites.  The violet cancels out the yellow.  It won't be pure white, but it won't be yellow, either.  I'd experiment with a single mix to see if you're happy with the results.