I think Franklin Pierce's obsession with annexing Cuba is a fun topic and could be a good topic for the classroom as Communist Cuba and its relationship with the US is well explored, but not always the earlier relationships. So here is some information on Piece's idea of annexation:
Far less successful was Pierce's pet cause—the annexation of Cuba. For years, southerners had coveted the great island as a place to expand their slavery-driven agricultural economy. Failed filibustering expeditions during the Taylor and Fillmore presidencies were evidence of the South's attempts to obtain this slaveholding Caribbean possession of Spain.
Southern interests in Cuba were understandable. After all, that nation allowed slavery and was developing a plantation form of agriculture, and would continue to do so until two decades after the Civil War.
During Pierce's administration, many Americans reasoned that if Cuba were to be purchased from Spain, they would in effect have another slave state. The wrong man was charged with the delicate task of negotiating with Spain's poor but proud king. Pierre Soulé, an overbearing southerner, had been named
Pierce's minister to Spain, with instructions to go as high as $130 million, but Soulé had little patience for the slow ways of the Spanish court. The more he tried to bully Spain into selling Cuba, the more that nation resisted the idea. Soulé even rewrote the treaty to include threats of American military action if Spain did not comply, which only stiffened Spanish resolve. Soulé met with James Buchanan, Pierce's ambassador to England and future President of the United States, and John Mason, the minister to France. Together, they drafted the Ostend Manifesto, a document that set the justifications for American possession. The Manifesto also warned that if Cuba refused America's proposal, "internal peace" in the United States might be threatened by continued Spanish control, since slaves might revolt on the island, threatening the institution of slavery in the U.S. Under such circumstances, America might be required to take control of Cuba. After the document was published, Pierce's secretary of state, William Marcy, was forced to repudiate the Manifesto because of the diplomatic uproar in Europe and in the north that ensued.
If you'd like a primary source, chekc out this statement from Pierce telling citizens not to invade Cuba on their own! He also issued proclamations not to invade Nicaragua and Mexico as well!