In 1900, the United States still controlled Cuba. After the Spanish-American War, the United States began a military occupation of the island. This lasted until 1901.
That year, the Cuban Constitutional Convention adopted a constitution written by the US which contained acceptance of the Platt Amendment. The United States considered the Cuban people unfit to govern themselves, and wanted to profit off Cuba.
Tomás Estrada Palma became President in 1902. He lasted until his resignation in 1906. Like many Presidents to come, he was paid and completely controlled by the United States.
His resignation in time of violence caused another US occupation, this one headed by Charles Magoon. After the Americans left again, José Miguel Gómez was elected. He remained for one four-year term.
Gómez was well-liked and seen as having better intentions than some other Presidents, but did use office to make himself rich.
During this period the United States sent in troops occasionally. It wanted to protect its business interests, and sent troops in 1912 and 1917.
The next Cuban President was Mario Menocal, a general. He lasted for two terms, from 1913 to 1921. During this time, World War 1 caused the price of sugar to reach record levels. Worth as much as 22.5 cents during wartime, it fell to 3.625 cents by 1921.
After Menocal, Alfredo Zayas became President (quite possibly unfairly). His single term until 1925 was also used for personal enrichment. When he decided not to run again, Gerardo Machado y Morales was elected.