Cuba gets independence on its own

Let's say the War of Cuban Independence concludes succesfully before the US has a chance to intervene, or the war goes as OTL but the US decides not to intervene at all. What would relations be like between independent Cuba and the US? And would Puerto Rico be joined with Cuba in a single country, or become independent on its own? Also, how would no Spanish-American war effect the politics and culture of the US, Spain, Cuba, and Puerto Rico?
 
Maybe, if Mexico did it on her own, I don't see why Cuba couldn't, however they'd have to do it at a time when Spain was distracted, like during the Carlist Wars.
 
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