The phrase 'eclectic mix of cultures' is correct and can be used in written English. You can use it to refer to a wide variety of different cultures that come together in one place or situation. For example, "The city contains an eclectic mix of cultures, making it a great destination for travelers".
In Paris the Barbès quarter is known for its eclectic mix of cultures, especially when it comes to music.
His friends, from an eclectic mix of cultures and ages, will miss his generosity, passion, intellectual curiosity, wisdom and, I dare say it, greatness.
At ASA, there is an eclectic mix of cultures and outlooks, and classroom discussions can be illuminating and educational in a way that few other schools can match.
What I love most about it, however, is it perfectly sums up what Los Angeles really is: an eclectic mix of cultures, cuisines and diversions.
Not all festivals have the eclectic mix of arts and culture of Latitude that keeps the crowds flocking; 2011 was a particularly disastrous season, with 30 music festivals cancelled and even Glastonbury's Michael Eavis predicting his mighty event's demise in a few years' time (although that looks unlikely to be the case).
It's a dependable source of surprise, puzzlement, irritation and delight, offering an eclectic mix of rising local talent, offbeat takes on popular culture and notable but not quite household-name artists from all over the world.
We love to be in culture spheres, areas that are redeveloping, that have an eclectic mix of residential, commercial, arts and restaurants, areas where there is a vibe.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union