In 1956 CONMEBOL, the South American confederation, organized a cup who's purpose was to strengthen the competition between the continent's strongest nations: Brazil, Argentina and Uruguay. Paraguay was later included as well after the first edition.
The Atlantic Cup was played three times, one in 1956, then in 1960 and lastly in 1976. In all three occasions Brazil took the title with Argentina coming second, while Uruguay and Paraguay alternated between 3rd and 4th place.
The first edition in 1956 also featured a parallel cup for clubs, the Atlantic Cup for Clubs which featured five clubs from each of the three participating nations. The final between Corinthians and Boca Juniors was mysteriously never played. It is said that Boca refused the play because if after the two legs a winner wasn't crowned the tiebreaker would be a third match played in Brazil. There are rumors that CONMEBOL took Boca's decision as a forfeit and gave Corinthians the title. There is another rumor that the first match was played in Argentina and Corinthians came out with 3-2 victory. None of these rumors have any solid evidence supporting them and if you ask the confederation, or either club, they'll all say there simply was no champion.
The Atlantic Cup for Clubs died 1956, the Atlantic Cup for national teams however continued in 1960 and was executed smoothly. Later the cup began to loose relevance and purpose most likely due to the growth and consolidation of the FIFA World Cup and the Copa America. There was one last attempt 16 years later in 1976 and the interesting thing about that specific Atlantic Cup was that every match-up between Brazil and another country was also worth a trophy within itself.
Brazil vs Argentina was the Superclassico of the Americas, Brazil vs Uruguay was the Copa Rio Branco and Brazil vs Paraguay was the Copa Oswaldo Cruz. All three of these cups had a lot of history and had been held for decades, so including them within the Atlantic Cup was clearly a way to revive the tournament by giving it added importance. The desperate attempt wasn't successful and 1976 marked the last time any of the aforementioned cups were ever played, except for the Superclassico which was revived in 2011 but discontinued again in 2014.