Do Cuban-Americans wield significant amount of influence in US politics?
Cuban-Americans influence U.S. politics because the two-thirds of them who live in Florida often play a deciding role in that state's politics.
Since at least the 2000 election Florida has been seen as the most significant swing state in presidential elections. It awards 29 electoral votes--the third-largest number behind California and Texas. Unlike those two larger states, its choice has usually been determined by a very narrow margin. In 2016 Donald Trump won Florida by 100,000 votes.
Cuban-Americans make up around 1.5 million of Florida's 21 million citizens, enough to swing the state's close elections, which in turn have the potential to swing presidential elections overall, making Cuban-Americans an important demographic in national politics and a group courted assiduously by state and national candidates.