13 Sugarless Cakes for Baby's First Birthday - The traditional smash cake does not have to be high in sugar. Cakes can be sweetened with fruits, such as bananas, or even applesauce. Here you will find a list of 13 recipes for sugarless birthday cakes that are suitable for a baby's first birthday cake. Did I also mention that they are incredibly delicious? Studies show that kids shouldn't receive sugar until after 2 years ago and even then in small quantities.