accessibility Sums of cubes

The following results are all joint with Andrew R. Booker. We are very grateful for the assistance from our friends at Charity Engine.

     143075750505019222645^3 + (-143070303858622169975)^3 + (-6941531883806363291)^3
     569936821221962380720^3 + (-569936821113563493509)^3 + (-472715493453327032)^3
     (-385495523231271884)^3 + 383344975542639445^3 + 98422560467622814^3
     (-74924259395610397)^3 + 72054089679353378^3 + 35961979615356503^3
     (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3

     10378929361429825^3 + (-10007234208296573)^3 + 2(-3869419050286010)^3
     (-9766714092174289)^3 + 9706646342356061^3 + 2(2044177502818754)^3
     (-1274248491925945)^3 + 1094658539478551^3 + 2(723458325298043)^3
     (-1040743660046111)^3 + 1040742887519425^3 + 2(10786916701381)^3
     36330027574363^3 + 16201371125359^3 + 2(-29663565976595)^3