Question 1019845
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Prove that the number {{{ (2n+1)^3-(2n-1)^3 }}} can be written as the sum of three squares.
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Let me continue from the other post.


To complete the proof, we only need to represent 24n^2 + 2 as the sum of three square.


It is easy:


{{{24n^2 + 2}}} = {{{(4n^2 + 4n + 1)}}} + {{{(4n^2 - 4n + 1)}}} + {{{16n^2}}} = {{{(2n+1)^2}}} + {{{(2n-1)^2}}} + {{{(4n)^2}}}.


The statement is proved.