Whole Positive Number

Find three whole, positive numbers that have the same answer when multiplied together as when added together.




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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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I can turn polar bears white.
I can make anyone dance.
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I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
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