Why would the Confederates want Cuba though once the need for additional slave states to balance out the free states no longer applies? The Confederates aren't going to want to pay the taxes necessary to build the military that could seize Cuba. They aren't going to want to give significant political power to large numbers of Catholic Spainards (which would be necessary if Cuba is to ever be pacified). They aren't going to want to antagonize the British (who aren't likely to react well to a slave power miltiarily expanding). They aren't going to want to leave themselves exposed to being attacked by a revanchist US while their army is off fighting in Cuba. They aren't going to want to risk empowering a slave revolt in Cuba by weakening Spanish control. And Spanish controlled Cuba is actually very useful to the Confederates as long as the Spanish maintain slavery there because it makes the CSA less of a diplomatic pariah by having at least one western European nation that still practices slavery.
Perhaps, but isn't Confederate imperialism more likely to target Northern Mexico? It's sparsely populated, has some potential good cotton land, and will probably be much easier to seize than Cuba.
It's all Saber Tooth appetites on hamster teeth jaws. The Confederacy would, most likely be massively limited in its ability to rape its neighbors, near and far. The Confederacy for the most part is unlikely to afford a powerful navy, it's unlikely to afford or be willing to allow a powerful standing army, unless its perpetually facing a northern threat. If it is facing such a threat, it's going to be unlikely to hie off on military adventures elsewhere which would leave it vulnerable and potentially short of troops on the northern front. Without a northern threat, there's going to be insufficient motivation to invest in a powerful military, and there's going to be nonexistent ability or willingness to pursue the logistical wherewithal to be able to project such an army any distance for any length of time.
So the Rape of Cuba will not happen. The Sodomy of Santo Domingo, nadda. The purloining of Puerto Rico. The gutting of Guatemala. The nicking of Nicaragua. The Kidnapping of Costa Rica. The further despoiling and violation of Mexico. All these glorious acts in furtherance of the constitutional right to enslave black people, or at least to hang them like Christmas ornaments from trees, to steal, to rape, to rob, to bend those not white enough under the chains and jackboots of those sufficiently white, to cultivate the cult of subhumanity.... nope, not likely to happen.
Instead, the Confederacy, like any good junky, will dream glorious dreams, but ease back into genteel but ever more obvious shabby impoverishment, blissfully mainlining the blood and pain of black people into its veins to maintain it's high, and blaming everyone else in the world for its failures and problems.
That's whats likely to happen.
But hey, this is alt history, and people can write any confederacy at all, including one that successfully invades mexico and the caribbean multiple times, and gives all the former slaves ponies. If one works hard enoough, one can even make it plausible. Or at least entertaining. That's the beauty of it.