Prove Maasei hoshev

JoshC

I am taking a course in the history of modern math. Note, I am an engineering student minoring in math. Therefore, I am not that up to speed on induction proofs. I have been working on a problem in my book (A History of Mathematics by Victor Katz), and really don't know how to procede. Any help would be greatly appreciated.
Problem:
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Prove Proposition 32 of the Maasei hoshev (by Levi Ben Gerson):

1+(1+2)+(1+2+3)+...+(1+2+...+n)

={1^2+3^2+...+n^2 n odd;
{2^2+4^2+...+n^2 n even
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Thank you for your assistance

JoshC

Nevermind. I dropped the course. Thanks for the help.