It's often not easy to adapt your baking for special dietary requirements. It requires a long-term commitment to learning and experimenting, especially if you're cutting out crucial ingredients such as eggs. Boxed devil's food and other cake mixes provide a useful shortcut, while you relearn your baking skills. Boxed mixes contain a number of stabilizers and emulsifiers that can help mask the lack of eggs, and so they work with most of the common egg substitutes.
What Eggs Do
Eggs serve a number of roles in baking, providing richness, moisture and flavor to the batter. More importantly, they are integral to the chemistry and structure of your cake. The proteins in eggs -- along with the proteins in the flour -- contribute to forming your cake's crumb. Eggs also trap air when the batter is whipped, helping leaven the cake. Finally, emulsifiers in the egg yolk help the water-based and fat-based ingredients combine into a smooth-textured batter, which in turn results in cakes with a tight, soft, even crumb.
Puree is Simple
Your boxed devil's food cake mix has a number of additives to help it mix evenly, so focus on replacing the richness, moisture and flavor. One of the easiest ways to do this is with purees of fruit or vegetables. Applesauce and mashed bananas are two of the most versatile choices, because their flavors are compatible with most cakes. The rich chocolate flavor of a devil's food cake can also mask more daring choices, such as tomato puree or pureed cooked carrots. A standard-sized can of pumpkin puree added to your boxed mix can replace both the eggs and the oil. The finished cake will be slightly denser, but still very rich and flavorful.
Dairy and Non-Dairy Substitutes
A handful of dairy products and dairy substitutes can stand in for eggs in your boxed cake mix. Sour cream adds enough fat to compensate for the loss of the egg yolks, along with moisture and a rich tang that complements the chocolate flavor. Plain yogurt is a less-caloric alternative and adds enough protein to help compensate for the loss of your egg whites. Use soy-based replacements for yogurt and sour cream for vegan baking, or if you're accommodating both egg and dairy allergies. Many bakers use well-beaten silken tofu as a replacement for eggs in boxed mixes or other baked goods.
The egg substitutes sold in your supermarket's dairy case are usually made with egg whites, so they aren't a true replacement. Real egg replacements use a variety of natural starches and gums to simulate the binding effect of the eggs' proteins. Achieve the same effect at home by mixing a paste of cornstarch and water to replace eggs, or using flax seed soaked in a small amount of water. Flax seed contains a natural gumming agent that helps improve your cakes' texture just as eggs do.