Three Digit Number

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?




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What are the next two letters in the following series and why?
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*Hint: Check Puzzle Title

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Jigsaw puzzles

Jigsaw puzzles soared in popularity during the great depression, as they provided a cheap, long-lasting, recyclable form of entertainment.