Next in the Series

Find the next number in the series?
2, 12, 36, 80, 150, 252, 392, _ ?




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Sherlock is somehow able to deduce that the man who stole the cat is telling a lie and the man who stole the hen is telling truth.

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Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

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There was a greenhouse.
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