In EU4, I was considering performing a colonial Japan campaign with the eventual goal of creating a Mexican empire with the culture of Japan. But is it necessary for a nation to have a western culture to form the nation, our can I do it with any country?
You can form a colonial nation as Japan. The only requirement you have to fulfill is that your capital may not be in a colonial region itself.
As all colonial regions except for Australia are on the American continent, this means all nations starting in the Americas cannot form colonial nations, but all others can.