How does culture affect how great an empire is?

High levels of culture mean that the Empire is great because as we all know, culture spreads like wildfire. Soon when the Empire thinks of adding a province to its many provinces, it will be met with less struggle if its culture permeated that region. Most people would have been fearful of being invaded by a great empire solely because they saw that it would change their way of life and culture. But then again, that depended on what Empire we are discussing.