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The difference between cubic numbers gets larger as you go up the scale, so we know that we are looking for the small end of the range. Let's take a small set of perfect cubes and play with it:

- 125, -64, -27, -8, -1, 0, 1, 8, 27, 64, 125

27 + -8 would give us 0 would give us 16. And that would be our best option. Note of course that -27 + 8 would also fit the bill, giving us -16.

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Q: What is the smallest two-digit number that can be written as the sum of two different cubic numbers?
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