do these gods exist?

A question addressed to any religious people who may be so kind to answer it.

We are told that the Christian God and man share a likeness. We also know that throughout history many cultures have had Gods that are anthropomorphic, classical Greeks and Scandanavian Vikings being two of many examples.

My question is:

What happens to Gods when the cultures that believed in them no longer exist?

Do the Gods continue to exist and if so, for what purpose? Or if they no longer exist then doesn't that infer that a God is only relevant to the culture that manifests it their minds, and therefore cannot exist without that culture needed to create it.

Any thoughts?