What was the year Cuba became US territory?
It wasn't. It was granted Independence from Spain under the 1898 Treaty of Paris.
As a result of the Spanish-American War, 1898 the US occupied Guam, the Philippine Islands, Puerto Rico, and Cuba. The US purchased the Philippine Islands for $20,000 and became independent in 1948; Cuba became a protectorate of the US but obtained its independence from Spain; and Guam became a territory of the US as well as Puerto Rico.