Is creativity part of human nature or is it something that must be nurtured and learned?

Both.  Some people are more creative than others from birth, but that creativity must be nurtured for it to reach its full potential.

It's both.

Not everyone is creative.  But any degree of creativity grows and develops if it's encouraged - if the person has the opportunity to find out what they're capable of, has access to learning how to create and if they choose to allow themselves to grow and develop.