Tricky one, on one hand they didn't get what they ordered, on the other hand, did they return it or eat it once they realised it was the wrong cake?
I think if they ate the cake then a part refund is in order, if they return the cake to you relatively uneaten (no doubt a little was eaten before they realised the error) then a full refund.
What flavour did they order and what did they get?
i'm with bubs -- partial if they ate it -- you don't get free cake -- maximum half off -- but start with 10% --
when I clean house and sort stuff to be given to goodwill -- I have to get my mean face on just so I can part with stuff -- know what I mean -- so get your inner mean face on and deal with these people --
LOL! -K8memphis, maybe that what I need to do so I can get rid of junk, get my mean face on! I am such a packrat!
sandra -- hahahaha -- I just gotta get real mean inside -- or it won't work -- I can think of a thousand purposes for everything -- and I worked hard to get all of it in the first place so... ain't easy -- ha! 
grace24 -- let me know how it goes -- I hope you don't have to refund too much 
I did something similar this week. A customer ordered a plain birthday cake. Nothing special. Just said Happy Birthday. My husband was running the register and sold the cake to someone else not knowing it was sold. ( my fault for not putting the name on immediately when I finished). The customer showed up an hour later and I couldn't locate her cake. Finally my hubby told me what he had done. The customer went home sad. Not mad, just sad. An hour later, my conscious was bothering me so much. So i called her and told her to tell me whatever cake she'd like that was in the same price range, it'd be free and I would bring it to her. She was so thankful and it made me feel good inside. I figured that it would pay off in the long run as she'd tell her friends and family what great customer service we provided by making it right. It only cost me about $20 and an hour or so. Worth that and more to keep a customer happy and one who will return.
On the same note, I had a customer who didn't make it clear that she wanted nuts on her cake. She kept saying she wanted the one with she always gets and with the "topping". Well her cake she always orders doesn't have any sort of "topping" so I made her usual order. So she picks it up and blesses out my cashier saying it's not her usual cake. Then she emails me over and over before I even knew there was a problem. When I don't answer the emails right away cause I'm at the dentist, she calls back and wants to know where her "nut" was. LOL. Then she gets on FB, posts a pic of her cake, tags me in it and says , "My cake was supposed to be like but with a "nut". LOL. She aggravated me and my shop enough that I don't care if she returns ever. I think she already has her "nut".
I had something similar happen. The woman said it was the wrong chocolate forsting. I told her to bring back the un-eaten portion of the cake and I would give them a refund. They brought back 1/4th of a 10" cake! There were only 6 people! Unfortunatley, I gave them back a full refund. Thinking back, I should have only given them 25% due to the 25% they returned. I slam dunked the bugger into the trash dumpster outside. It felt so good to be rid of the whole ordeal.
I don't think I would refund the cake if they ate the whole cake. How about a 20% discount on their next order?
No one is perfect, we all make mistakes!
Quote by @%username% on %date%
%body%