Cuba already had slavery, and indeed didn't give it up till 1886.
Certain southerners had delusions that after independence they would be able to expand militarily into the Caribbean, Mexico, and Central/South America, creating a great slave empire.
But it was never more than delusion. Such expansion, given the transport tech of the time, could only be by sea. And the Royal Navy, not to mention the US Navy, would never have allowed it.
“Cuba already had slavery, and indeed didn’t give it up till 1886.”
Nor did the United States until after the war. The war was an apostate puritans’ honor killing. The Salem witch trials writ large, but this time in the service of secular power.