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.