Cake Item and Cake Block have no identifying ingame features (cannot use in /replaceitem)

I know that this is technically "Works As Intended" (as was the ID for cooked fish being minecraft:cooked_fished before it was fixed). However, I am attempting to make an adventure map that includes a layer cake. I realized that both the cake item and cake block have the ingame ID of minecraft:cake. This means I cannot use /replaceitem to put it on an armor stand to make the cake.