Waring It Well
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All natural numbers can be written as the sum of cubes of other natural numbers.
37 = 27 + 8 + 1 + 1 = 3^3 + 2^3 + 1^3 + 1^3
All but two natural numbers can be written as the sum of eight or fewer cubes.
Two numbers require the sum of at least nine cubes.
a) One such number is 239. Write 239 as the sum of nine cubes.
b) What is the other natural number that requires a sum of at least nine cubes?
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