The USA is leading country in military expenditure in the world. To match what the USA spends you have to add up the budget of the next 11 countries on the list combined. ref here
The USA is not just the most militaristic nation on earth but also the first world cultural superpower. The whole world is flooded American films, music, news, fashion, architecture, foods, etc. Even American English is the international language nowadays. In most mainstream literature and art this country is generally portrayed as the hero country of the world givers of freedom and capitalistic prosperity. It's rare to find cases in which the Americans are portrayed as villains not even in non-American films.
In history American culture (mainly Hollywood) has tried to offer an unrealistic vision of the world through art and propaganda which antagonises those considered enemies or apathetic to their Anglo-capitalistic agenda whose distortion of reality still remains up until today. ex. (Native Indians, African slavery, Socialism, Communism, Spanish-American war, The Japanese during WWII, the Vietnam war, The Russians, The Iraqis, The Iranians, etc.)
The relationship between culture and military power is nothing new. The Romans took a great deal of culture from the Greeks and the Roman Empire influenced culturally not just their colonies but neighbouring areas.
Are there any books, films authors etc who ponder on how culture is power and vice-versa?
- Sid Meier's Civilization® is an strategy game about world domination. In this game you can also achieve a cultural victory