Crossword Genius

What's after May first and second in Cuban capital city (6)

Ross

I believe the answer is:

juneau

I'm a little stuck... Click here to teach me more about this clue!

'capital city' is the definition.
'Juneau' can be an answer for 'city' (Juneau is an example). I am not certain of the 'capital' bit.

'what's after may first and second in cuban' is the wordplay.
'what's after may' becomes 'june' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'first and' becomes 'a' (jst letter of 'and').
'second in cuban' becomes 'u' (und letter of 'cuban').
'june'+'a'+'u'='JUNEAU'

Can you help me to learn more?

(Other definitions for juneau that I've seen before include "Capital of Alaska" , "Alaskan port" , "state capital" .)

I've seen this clue in The Times.
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