First of all, WE are not doing anything. The U.S. government is. It should legally be my government, certainly, but it doesn't do what I want and I do not identify with its actions to the point of using a first-person pronoun. I'm sorry that you suffer from such an identification. Odds are, IT is not blockading Cuba for your benefit!
In 2012, for something like the 20th consecutive year, a record 188 members of the United Nations voted in favor of a Cuban resolution to "put an end to the economic, commercial and financial blockade imposed by the United States of America against Cuba." http://www.cubaminrex.cu/en/cuban-ambassador-jamaica-offers-radio-interview-recent-endorsement-un-resolution-against-us-blockade
Embargo has the too-gentle connotation of one country refusing to do business on legitimate grounds. A blockade need not involve a total physical blocking of the ways into and out of the island. In the past, of course - even before the missile crisis, one might add - the U.S. imposed such full physical blockades. The U.S. policy of sanctions, reinforced since 1996, is highly damaging, aggressive and international, and seeks to coerce other countries to go along -- by imposing regulations on subsidiaries incorporated in other countries, and by abusing NAFTA and WTO into instruments of the economic blockade. Therefore the legitimate aggrieved party in this matter, the attacked nation of Cuba, prefers the term of blockade. I respect that.
Here's a discussion of the matter by a U.S. scholar who prefers the "embargo" term, but makes clear the myriad ways in which the policy goes beyond the harmless-sounding "embargo," the damage done to Cuba, and also how regime change is explicitly enshrined as the goal in the letter of the law.
Berta Esperanza Hernández-Truyol, Embargo or Blockade? The Legal and Moral Dimensions of the U.S. Economic Sanctions on Cuba, 4 Intercultural Hum. Rts. L. Rev. 53 (2009).
http://scholarship.law.ufl.edu/cgi/viewcontent.cgi?article=1219&context=facultypub