New Figurate Number Relation? [closed]

Has anyone seen the relation $$nP_{2}(n)=P_{3}(n-1)+\sum_{i=1}^ni^2$$ where $P_2(n)$ is the $n$th triangular number and $P_3(n)$ is the $n$th tetrahedral number?

I know the straightforward algebra proof, and I have the geometric proof, but I was wondering where, if at all, this may have been in the literature? Thanks.

closed as off-topic by Isaac Browne, Namaste, Shailesh, Xander Henderson, user21820Jul 2 '18 at 9:46

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