Math is Beautiful

Go on, whip out that calculator and confirm the mathemagical equation above. From @Pickover.

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So then this raises the question, is there more than one answer for any known value of m, where m is the number of iterations on the left side of the equation? In other words...

n^2 + (n+1)^2 + ... + (n+m)^2 = (n+m+1)^2 + ... + (n+2m)^2
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I wonder if there are more, or even infintely many instances of this pattern, or if this is the only one...

n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = (n+4)^2 + (n+5)^2 + (n+6)^2

I would have no idea how to approach it. Somebody get Numberphile, or Mathologer, or Singing Banana on this!!!
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