Like they said in your first query, I don't think such a work exists. You're talking about the Spanish, French, Portuguese, British, American, and Mexican governments and citizens (not to mention more than 20 Central and South American and Caribbean nations that gained independence in the 18-20th centuries), spanning an entire hemisphere and 500 years. Extrapolating from your example - a 3-part history of the Third Reich (1933-1945, so 4 years per volume) - a comparable history would be 125 volumes, and almost necessarily more, given the geographic scope. If you can narrow your focus to a time and place, there's probably something out there. You might check out the book list as well and see if anything there piques your interest.