I have a special request for a black licorice cake and I cannot for the life of me find a recipe for one!! Please help 
All I can say is **YUCK!!**
I would use a white mix/recipe and chop some (up to 1 C?) blk licorice.
I know of a place in IN that sells many different, very unusual flavorings. You might do an internet search to see if you can find some. Maybe candy flavoring (LorAnn is one brand). It is usually very strong so use just a couple of drops until it smells or tastes as you want. Good luck
Anise seed or oil may give you enough licorice flavor, if just added to an otherwise vanilla cake. I'd be really subtle with it though, or it'll start to taste more medicinal.
And for the record...ugh, that wouldn't appeal to me AT ALL! But, sure hope that it works for you!! 
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