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%I #7 Feb 01 2021 18:11:34
%S 28,126,152,344,370,468,730,756,854,1072,1332,1358,1456,1674,2060,
%T 2198,2224,2322,2540,2926,3376,3402,3500,3528,3718,4104,4706,4914,
%U 4940,5038,5256,5572,5642,6244,6860,6886,6984,7110,7202,7588,8190,8288,9056,9262,9288,9386
%N Sums of two distinct odd cubes.
%e 126 is in the sequence since 1^3 + 5^3 = 1 + 125 = 126, where 1 and 125 are two distinct odd cubes.
%t Table[If[Sum[Mod[i, 2] Mod[n - i, 2] (Floor[i^(1/3)] - Floor[(i - 1)^(1/3)]) (Floor[(n - i)^(1/3)] - Floor[(n - i - 1)^(1/3)]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 1200}] // Flatten
%Y Cf. A000578, A010057, A339990.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Dec 25 2020