Since this is sum is a p-series with p>1, it does converge. Unfortunately, there is no precise way to arrive at the limit of a p-series sum, so it must be approximated. If you want to approximate it yourself, you can look up methods to do so. I simply utilized Wolfram Alpha to find that the limit of this series is approximately 1.20206.
@laureth To have a sum, you’d need to know when to stop adding, an end point. An infinite problem, by definition, does not have that. Actually, many infinite series do converge to a specific number. Of those, some can be solved precisely, but most must be approximated. Fortunately, they can be approximated to any desired margin of error (except zero error, of course).
@hiphiphopflipflapflop While you are correct about the harmonic series, that is not the series in question. The OP asked about n^(-3), not n^(-1).