The restoration of cooperation and political dialogue between the European Union and Cuba (EU-Cuba) in 2008 crystallized in 2016 with the creation and launch of the New EU-Cuba Cooperation Model (EU-Cuba NCM). (1) The NCM is characterized by strengthening relations between both parties through political dialogue, cooperation, trade, and human rights under equal conditions and without any interference in the internal affairs of the parties; (2) for configuring a political-institutional-legal space that responds to the interests of Cuban and European societies; and (3) allowing the EU to accompany the transformations that the government and the Cuban society have been carrying out since 2011 in their economic-social-political model to guarantee greater well-being, a better redistribution of resources, and sustainable development in their society. In fact, it facilitated the repeal of the EU Common Position against Cuba; the implementation of 120 projects worth €300 million; and the signing and provisional application of the first EU-Cuba Political Dialogue and Cooperation Agreement of 2016. The work analyzes from the institutional approach the positive effect of the NCM in reducing social inequalities in Cuba and how this model is being replicated since 2020 in the EU-Venezuela relationship—especially, since Covid-19, affecting regional cooperation programs related to sustainable development, in the Caribbean and Latin America. The analysis is structured in three sections. The first analyzes the characteristics of the NCM and the impact on Cuban society, from its start-up; the second analyzes the challenges faced by the EU-Cuba NCM to replicate its model in the relationship in LAC through Triangular Cooperation; finally, it is concluded that the implementation of the EU-Cuba NCM has been revealed as the most effective tool to strengthen the EU’s bilateral and multilateral cooperation and work to eliminate inequalities in LAC.