Isaac Newton did number theory?!

I was reading Whiteside's article called "Newton the Mathemtician", where he says that Newton did Number Theory (e.g. inverstigating which numbers are expressible as a sum of two cubes). If this is true, can someone point me towards some papers of newton on number theory? If not, then do you know which book in the eight-volume Newton's mathematical papers I can find his number theory work? I'm very interested in this, it came as a huge surprise (perhaps it shouldn't have) to me that Newton even knew of number theory.

Concrete questions:

1. Where can I find Newton's number theoeretical work in Whiteside's "Newton's Mathematical Papers" volumes?
2. What did Newton investigate in Number Theory, and what did he discover?

Thanks!

EDIT: Here is the extract from Whiteside's article where he talks about Newton doing NT:

I would have written this in a comment but I don't have the rep yet.

In Stillwell's beautiful article about elliptic curves (in the also great book Mathematical Evolutions) he cites a paper where Newton recognizes Diophantus parametrization of the cubic $x^3-3x^2+3x+1=y^2$ as a use of geometry to get results in number theory (you can find the bibliographical reference in the last page of the linked article)