201 years ago today, on October 4, 1824 (August 12, 1824 lunar calendar), Mexico was established as a republic. National Emblem On October 4, 1824, Mexico was established as a republic. The United States of Mexico is located in North America, bordering the United States to the north, Guatemala and Belize to the southeast, the Pacific Ocean to the west, and the Gulf of Mexico and the Caribbean Sea to the east. Capital Mexico City. Comment: It was only in the 1860s that the Mexican people finally drove out the invaders.