# Ramanujan might take a little longer on this one

This problem is a much more difficult computer-science follow-up to this question. If you have already read the paragraph about Ramanujan there, you can skip it here.

Today, Sunday, December $$22$$, is Srinivasa Ramanujan's $$126\text{th}$$ birthday. Ramanujan was an amazing mathematician, but one of the things he was most famous for had to do with the number $$1729$$. When Ramanujan was in the hospital, he was visited by his friend G.H. Hardy. Hardy remarked that the taxicab that he had ridden in had a rather uninteresting number: $$1729$$. Ramanujan said that no, $$1729$$ was very interesting because it was the smallest number that can be expressed as the sum of $$2$$ cubes in $$2$$ different ways. These are $$12^3+1^3$$ and $$10^3+9^3$$. Hence, numbers that can be written as the sum of multiple cubes in more than $$1$$ way are called taxicab numbers. Some more really interesting information about taxicab numbers can be found in this video.

So here's the problem.

Let $$f(n)$$ be a function that finds the sum of the digits of $$n$$. What are the last $$3$$ digits of this expression? $\sum_{i=1}^{17}\sum_{j=1}^{29} f(i^3+j^3)$

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