Yes, you can add whole egg instead of just the whites to a boxed white cake mix. It will just not technically be a "white" cake anymore though- those yolks will give it a slight yellow tinge and slightly change the texture of the final cake. As far as adding cherries- that depends. The juice from canned, jarred, fresh or frozen cherries can over saturate your mix, and leave you with a wet stodgy end result. There are recipes for something called a cherry dump cake though, which use cherries in all those forms, and a cake mix to produce fairly yummy results. You can also add fresh halved cherries to a regular mixed box cake mix, after you lightly coat them with flour. They still might sink to the bottom somewhat, but you do end up with a nice cake otherwise. I've never tried using frozen cherries, so don't know what those would do- but I suspect it might leave you with a soggy mess on the bottom. If I were you, I would probably opt for the cherry dump cake recipe that called for cherries in the form you have, and would use whole eggs as well.
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Rather, use them to make a frosting or a puree to serve with the cake.
Or some kind of compote to put between two layers.