Final answer:
Cuba was the colony of Spain that gained freedom after the Spanish-American War of 1898. Post-war, Spain recognized Cuba's independence and ceded other territories to the United States, which then exercised significant influence over Cuban affairs for years through the Platt Amendment.
Step-by-step explanation:
The colony that gained freedom following the Spanish-American War was Cuba. Cuba was one of Spain's last colonies, alongside Puerto Rico, the Philippines, and Guam when it rose to prominence after Columbus's discovery of the New World in 1492. During the Spanish-American War, Cuba's quest for independence became intertwined with the United States' military engagement against Spain.
After a swift and decisive victory by U.S. naval forces in both the Caribbean and the Philippines, Spain capitulated and recognized Cuba's independence in the Treaty of Paris in December 1898. Subsequently, the United States acquired other Spanish possessions including Puerto Rico, Guam, and the Philippines. Although Cuba declared independence in 1902, it remained under significant U.S. influence, with the Platt Amendment allowing the United States to intervene in Cuban affairs.
Nearing the close of the 19th century, the defeat of Spain by the United States effectively ended the Spanish colonial empire. The war marked a pivotal shift in both nations' histories, with Spain receding from its role as a global colonial power and the United States beginning to establish itself as a significant force in international geopolitics.