Freedom to Export to Cuba Act of 2021 This bill repeals both the President's statutory authority to impose an embargo on Cuba and various prohibitions against providing assistance to Cuba. It also repeals provisions related to (1) the President's authority to impose sanctions on countries that provide assistance to Cuba, (2) the prohibition against U.S. investment in domestic telecommunications networks within Cuba, (3) restrictions on vessels that have departed from a port in Cuba within 180 days of loading or unloading freight in the United States, and (4) restrictions on remittances to Cuba. The President is authorized to impose export controls with respect to Cuba and exercise certain emergency economic powers in relation to unusual and extraordinary threats to the United States.