Many a sweet tree falls down (8)

I believe the answer is:

gumdrops

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'many a sweet' is the definition.
I can't tell whether this defines the answer.

'tree falls down' is the wordplay.
'tree' becomes 'gum' (gum tree is a kind of tree).
'falls down' becomes 'drops'.
'gum'+'drops'='GUMDROPS'

Can you help me to learn more?

(Other definitions for gumdrops that I've seen before include "Sweets" , "confectionery?" , "Gelatinous sweeties" .)

I've seen this clue in the Sydney Morning Herald.

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