You can make a box cake without eggs but the box cake will fall apart and not hold up very well.
If you want your box cake or cake to turn out properly and turn out to be a good cake then you should always add some egg to the box cake or other cake mix as it helps the cake hold together and adds moisture to the cake.
Eggs when added to cakes helps the cake hold together and not fall apart as the eggs help bind the cake together.
If you bake the cake without eggs the cake will not turn out very good and may fall apart.
The eggs in cakes and other baked goods are very important at making the cake turn out good as well as any other baked goods.
The eggs when added to cakes help to bind the cake together as well as create structure and stability within the cake batter.
The eggs also help add moisture to the cake which is also important and also help to glue the cake together so that it doesn't fall apart.
You can make a cake without eggs but the cake will not turn out very good.