I want to visit Cuba, I am paying for lodging and flights through my computer in the US, the flight that I want fly from Mexico to Cuba, so I will be traveling by car to Mexico to visit some family and then fly to Cuba, should I travel to Cuba as a US Resident or with my Mexican citizenship? Also do I have to tell the officer crossing back to the US in the border I went to Cuba or just Mexico?
You say "US resident" - do you have a US passport ?
Does Mexico have rules about using your Mexican passport to enter and leave there ?

US Resident as a Permanent Resident "Green Card", and to enter and leave Cuba? no rules just passport and insurance.
Cuba - passport, tourist visa and insurance.
Your green card is irrelevant as far as Cuba is concerned.
If you're asked by law enforcement,customs, where you went you're obligated to tell them by law where you went, what you decide to do is your business.
You are in your car at the Mexican-US border. You would tell US Immigration, you were in Mexico City and any other cities/town in Mexico you visited. If you said also Cuba, the US agent would say , "So what". They don't care.
Hi! It shouldn't really matter. In fact, because you're not a US citizen, it's likely even less of an issue since technically US rules on Cuba travel only apply to citizens.
When we returned from Cuba in March, I went through the expedited Global Entry line while my friends went through the regular customs lines. None of us were questioned other than being asked if we brought back anything. I told the customs agent I bought some cigars as gifts and some rum at the duty-free store at the airport and I was stamped and processed within 30 seconds.
I wrote up these Cuba planning tips at the request of friends and coworkers, hope they can help you a bit as well! http://www.anomadontheloose.com/cuba-travel-planning-tips/
... since technically US rules on Cuba travel only apply to citizens.
Actually, that is incorrect. US rules on travel to Cuba apply to all residents of the USA, even if they are not US citizens. (As do all US laws, in fact.)
I was told that by Southwest and American Airlines agents but if I'm wrong, I stand corrected!
§515.329 Person subject to the jurisdiction of the United States; person subject to U.S. jurisdiction.
The terms person subject to the jurisdiction of the United States and person subject to U.S. jurisdiction include:
(a) Any individual, wherever located, who is a citizen or resident of the United States;
(b) Any person within the United States as defined in §515.330