Who is Gandalf's and Radagast's common ancestor?

[Meriadoc1961]

In The Hobbit as Gandalf is leading the Dwarves and Bilbo to Beorn's house, Gandalf refers to Radagast as his cousin. Just who is the common ancestor of Gandalf and Radagast that would make them cousins? Who are their parents?

[Morwen]

Well they are both Maiar created by Eru so I don't think that you can take Gandalf's description literally. I suppose this may be cited as one of those instances where "The Hobbit" does not align with the Legendarium.

[Legate of Amon Lanc]

No one, of course. The term "cousin" is used here to explain to an "earthly" person (Beorn) that Gandalf and Radagast are not just friends, but are of the same origin. The Wizards, or Istari how they were called by the Elves, were in fact "angelic" beings sent to Middle-Earth to help the Free Peoples, but their origin was far before the Time. The term "cousin" is quite proper in this case: as the Maiar spirits, both Olórin (Gandalf) and Aiwendil (Radagast) belonged to one of the Valar, and had they belonged to the people of the same Vala, they could have been called "brothers". Now, since they belonged each to someone else, they could be called "cousins". In this terminology, their common "grandfather" was Eru Ilúvatar, the omnicreator (though that's not correct, because Valar and Maiar differ only in power and they all were originally equals created by Eru before the beginning of times).
In this way, Saruman was also Gandalf's "cousin". Interestingly enough, the same could be used, in this terminology, for the Balrog or even Sauron. The fact that we never hear from Gandalf "and perhaps you know my bad cousin Sauron, who lives in that black tower far to the South" or "look, Legolas, it's my cousin Balrog" is partially due to the fact that Morgoth, to whom both of the named belong(ed), is "no longer counted among Valar" (as Valaquenta says).

[Annatar]

Originally Posted by Meriadoc1961

In The Hobbit as Gandalf is leading the Dwarves and Bilbo to Beorn's house, Gandalf refers to Radagast as his cousin. Just who is the common ancestor of Gandalf and Radagast that would make them cousins? Who are their parents?

Well, given Gandalf's origin as a Maia, I would say it's a term of respect.

[Meriadoc1961]

I have considered the possibilities expressed so far, but I have also thought of another explanation: it is simply a "mistake" made by Tolkien. By "mistake" I mean I believe he wrote The Hobbit independently and the rest of LotR and The Silmariliion followed from its success, and he tied it all together. I believe at the time he wrote The Hobbit that he had not considered to the extent he later did the origins of wizards. He may have thought they were merely old, wise men with magical arts and abilities. Therefore, he and Radagast easily could have been cousins in the literal, physical sense of the word with grandparents as the common ancestors when he first wrote that they were cousins.

Merry:

[Legate of Amon Lanc]

Well, of course. But in that case I don't suppose that Tolkien had any ancestor made up for them.

[William Cloud Hicklin]

Actually Tolkien here as so often was using a word in its older sense: cousin meant generically "kinsman," without implying a particular relationship. (So also did 'nephew', which meant only younger male relative- hence T's preference for the more specific 'sister-son.')

Of course, externally it's the case that when T wrote the passage he had no idea that Gandalf was anything other than a Man with magical abilities.