They're forbidden to eat bun's filling in American cakes (6)

'american cakes' is the definition.
'donuts' can be an answer for 'cakes' (donut is a kind of cake). I am not sure about the 'american' bit.

'they're forbidden to eat bun's filling' is the wordplay.
'they're forbidden' becomes 'donts' (as in 'dos and don'ts').
'to eat' means one lot of letters goes inside another.
'filling' says to take the centre (the letters which fill the word).
The central letter of 'bun' is 'u'.
'donts' placed around 'u' is 'DONUTS'.

'in' is the link.

Can you help me to learn more?