Answer :
I would say that the following sounds correct:
Mexico City, the capital, is also the cultural center of the country
Mexico City is the noun clause and the capital is the appositive (restates the noun clause). If you read it out loud the pauses that you have in this sentence makes sense. Hopefully this helps. If not please let me know and I'll try to explain it better. :)
Mexico City, the capital, is also the cultural center center of the country.