Cakes currently have no assigned tool in the game even though it is a block (or slab) and mines the same speed as breaking wool with your hand.
Honeycomb blocks do not have an assigned tool
Turtle eggs do not have an assigned breaking tool
Glass blocks do not have an assigned tool
Cactus blocks do not have an assigned tool
Sea Lantern, Glowstone, Redstone Lamp don't have an assigned tool
Beds have no assigned tool