Filling it may be a piece of cake (5)

I believe the answer is:

mouth

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'piece of cake' is the definition.
'mouth' can be an answer for 'piece' (mouth is a kind of piece). I'm not sure about the 'of cake' bit.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for mouth that I've seen before include "Gob" , "Opening; say" , "trap" , "River part - conversation opener?" , "Opening of a bay" .)

I've seen this clue in the Evening Standard.

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