%I
%S 216,8000,64000,216000,343000,5832000,35937000,157464000,1540798875,
%T 3951805941,22069810125,23295638016,58230605376,170400029184,
%U 4767078987000,19814511816000,241152896222784,565199024832000,731189187729000,5399901725184000,13389040129314816,15517248640897024
%N Cubes that are also sums of three or more consecutive positive cubes.
%C Note that by Fermat's theorem no cube is the sum of two positive cubes.
%C All entries have the form A000537(j)  A000537(i1) with 1 <= i < j, for example (j,i) = (5,3), (14,11), (22,3), (30,6), (34,15), (69,6), (109,11).  _R. J. Mathar_, Sep 14 2007 [Presumably this comment refers just to the terms shown, and not to every term in the sequence.  _N. J. A. Sloane_, Dec 19 2015]
%C Subsequence of A265845 (numbers that are sums of consecutive positive cubes in more than one way) which is sparse: among the first 1000 terms of A265845, only 17 are cubes.  _Jonathan Sondow_, Jan 10 2016
%H Donovan Johnson, <a href="/A131643/b131643.txt">Table of n, a(n) for n = 1..55</a> (terms < 2*10^23)
%e 216 = 27 + 64 + 125.
%e Note that "positive" is needed in the definition, otherwise the sequence would contain 8 = (1)^3 + 0^3 + 1^3 + 2^3.  _N. J. A. Sloane_, Dec 19 2015
%t Select[Union[ Flatten[Table[ Plus @@ Table[i^3, {i, k, j}], {k, 1000}, {j, k + 1, 1000}]]], # <= 1000^3 && IntegerQ[ #^(1/3)] &]
%Y a(n) = A097811(n)^3.  _Donovan Johnson_, Nov 09 2012
%Y Cf. A000537, A265845.
%K nonn
%O 1,1
%A _Tanya Khovanova_, Sep 08 2007
%E More terms from _R. J. Mathar_, Sep 14 2007
%E More terms from _Donovan Johnson_, Mar 09 2008
%E Name edited by _Jon E. Schoenfield_, Dec 07 2015
