The goal (of a small number of mathematicians interested in that sort of problem) is to prove the hypothesis that all integers (except those congruent to 4 or 5 mod 9) can be written as a sum of three integer cubes. So in that sense this particular result has no value at all in achieving that goal. It might seem that it increases the probability of the hypothesis being true, but it really doesn't because it just demonstrates that one of an infinite number of integers satisfies the hypothesis.
So it's really just a bit of fun. Finding three-cube representations of specific integers doesn't help to prove the general case unless those representations reveal some kind of
pattern which mathematicians can work with.