Both. From 1521 to 1821 it was a Spanish colony; once it won its independence, Mexico became an empire (First Mexican Empire) until 1823, when it switched to a Republic.
Later, when France launched an invasion into Mexico, established a puppet government which was an empire (Second Mexican Empire). This empire lasted from 1864 to 1867 until Benito Juarez and his followers restored the Republic.
The Spanish Empire qualifies as such.
No country can be a colony, otherwise it wouldn't be a country.
Mexico was a colony of Spain.
The first European settlement in Australia was a penal colony.
France.
Brazil
At one time Mexico was a colony of Spain.
Bulgaria
france?
The Netherlands
Great Britain
Spain