How to find the sum of n natural logarithms that are cubed?

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KapitaiN

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Mar 14, 2020
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Hello! I seem to be struggling with a mathematical problem. I need to evaluate this:
Screenshot_9.jpg
I know that the sum of all natural logarithms is ln(n!) and that the sum of all natural cubes is (n(n+1)/2)^2 but these don't seem to be of any help in this situation. I would really appreciate some help!
 
I doubt there is any closed end formula, but building a table in excel is a snap.
 
I was able to find this from stack exchange:
Screenshot_10.jpg
But I am not yet familiar with Harmonic Numbers.
 
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