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 2222, is Srinivasa Ramanujan's 126th126\text{th} birthday. Ramanujan was an amazing mathematician, but one of the things he was most famous for had to do with the number 17291729. 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: 17291729. Ramanujan said that no, 17291729 was very interesting because it was the smallest number that can be expressed as the sum of 22 cubes in 22 different ways. These are 123+1312^3+1^3 and 103+9310^3+9^3. Hence, numbers that can be written as the sum of multiple cubes in more than 11 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)f(n) be a function that finds the sum of the digits of nn. What are the last 33 digits of this expression? i=117j=129f(i3+j3)\sum_{i=1}^{17}\sum_{j=1}^{29} f(i^3+j^3)

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