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In this video, the sum of logarithms of n cubed minus 1 divided by n cubed plus 1 from n equals 2 to infinity is calculated. The series converges with the integral test, but that is not the main focus. To evaluate the sum, rewrite it as the difference between the logarithms of n cubed minus 1 and n cubed plus 1. Factorize n cube minus 1 and n cubed plus 1 to simplify the expression. Split the logarithms into separate sums, factorizing the expressions further. This leads to two separate summations dealing with the terms separately.
