2008 iTest Problems/Problem 14

Problem

The sum of the two perfect cubes that are closest to $500$ is $343+512 = 855$ . Find the sum of the two perfect cubes that are closest to $2008$ .

Solution

Note that $10^3 = 1000$ and $20^3 = 8000$ , so check the first few cubes of numbers past $10$ . Since $12^3 = 1728$ and $13^3 = 2197$ , the sum of the perfect cubes closest to $2008$ is $1728+2197=\boxed{3925}$ .

2008 iTest (Problems)
Preceded by: Problem 13	Followed by: Problem 15
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2008 iTest Problems/Problem 14

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