How we cite our quotes: (Section)
Quote #1
That the government of Cuba shall never enter into any treaty or other compact with any foreign power or powers […] (I)
This quote shows that the U.S. is the exception. Congress is telling Cuba to not have any alliances, but of course this entire Platt Amendment required a treaty between Cuba and the U.S. That is not mentioned in this first rule, though. That is what we would call "implied power"—Congress doesn't even need to say "no treaties except for with us" because this is a power move. As though the treaty with the U.S. is so obvious and required that it doesn't even need to be mentioned.
Quote #2
That the government of Cuba consents that the United States may exercise the right to intervene […] for discharging the obligations with respect to Cuba imposed by the treaty of Paris on the United States […] (III)
American power on full display here. Yeah, Cuba's independent; but yes, the U.S. can get involved whenever it sees fit.
By bringing up the Treaty of Paris, the U.S. is reminding Cuba that the only reason it is free is because America defeated Spain. This mention serves as a warning about American power—"we booted out Spain, so we're tough and you owe us your allegiance." Lastly, using the word "obligation" makes America's power seem justified here, as though the U.S. is nobly protecting poor Cuba.
Quote #3
[…] the government of Cuba will sell or lease to the United States lands necessary for coaling or naval stations at certain specified points to be agreed upon with the President of the United States. (VII)
Let's focus on the naval stations part here. We can understand the U.S. wanting to put coaling stations on Cuba, in order to make some money. But naval stations? That sure seems like a pure power play.
Naval bases on the island would be both a show of power (thus keeping Cuba in line), and a clear message that America has dominance in the area (the Caribbean). If you put both the coaling and naval stations together, that's economic and military power in one fell swoop.