If someday, Mars were to become colonized by humans, would a baby born on Mars be considered a Martian?

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Any occupant of Mars would be Martian. 

(We are not talking about citizenship folks)

Depends on who (or what) was the father.

Maybe ask the IAU. They will screw up your head by declaring it is a "dwarf baby" for some bizarre reason.

When the North American British Colonies were still... err... British Colonies, was a baby born in Boston considered an American?

She would be considered British if she were born from British parents.  It is only after 1776 that Americans began to make a difference (and in 1783 for the rest of the world, with the Treaty of Paris).

Therefore, a baby would be considered a "Pink Skin" (Terran) until such time as Mars - or part of Mars - would consider itself a self-governing nation AND the nation(s) of Earth would accept the decision.

For white "Americans" born after 1776, the British considered them to be British citizens until 1783. This did lead to -- how should we say -- "misunderstandings".

Yes, of course. 

Yes. The definition of a Martian is an inhabitant of the planet Mars or a human colonist on Mars.

Yes it would.  There's an Antarctican person.

That is an interesting question as we would need to define what a human being is.  A baby born on Mars would have human DNA but the birth place makes him/her a Martian. "Stranger in a Strange Land" by Robert Heinlein asks the very same question.  

The child would be considered to be a Martian and rightfully so 

since his/her physicality, features, and skeletal structure would 

be quite different than those of an Earth child due to the difference 

in gravity. Bone density would be among the first things affected. 

I doubt we will colonize on mars, China maybe with forced labor with uighurs.