Unfortunately you can't pick up cake when it has been placed.
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Destroy it, then pick it up.
You have to make one and the combination on a crafting table is 3 buckets of milk, 2 sugar, 1 egg and 3 wheat
No, once placed a cake can't be moved. It has to be eaten, or destroyed.
Use a bucket
Mine it using a pickaxe (wood or better), then pick up the drop.