What are the mathematical steps used to get this $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$?

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I have accrossed this representation in cubic sum $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$ at this website but am confused how mathematicains proved this , Now Is this representation as cubic sum were proved using Computer or before using computer there are some theoritical steps which are used for application to computer ? And can someone use Wolfram mathematica for getting this kind of representation ?