0, 1, 2, 8, 9, 16, 27, 28, 35, 54, 64, 65, 72, 91, 125, 126, 128, 133, 152, 189, 216, 217, 224, 243, 250, 280, 341, 343, 344, 351, 370, 407, 432, 468, 512, 513, 520, 539, 559, 576, 637, 686, 728, 729, 730, 737, 756, 793, 854, 855, 945, 1000, 1001

Union[(#[[1]]^3+#[[2]]^3)&/@Tuples[Range[0,20],{2}]] (* _Harvey P. Dale_, Dec 04 2010 *)

is(n)=my(k1=ceil((n-1/2)^(1/3)), k2=floor((4*n+1/2)^(1/3)), L); fordiv(n,d,if(d>=k1 && d<=k2 && denominator(L=(d^2-n/d)/3)==1 && issquare(d^2-4*L), return(1))); 0
list(lim)=my(v=List());for(x=0,(lim+.5)^(1/3),for(y=0,min(x,(lim-x^3)^(1/3)),listput(v,x^3+y^3))); vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Jun 12 2012

is(n)=my(L=sqrtnint(n-1,3)+1,U=sqrtnint(4*n,3));fordiv(n,m,if(L<=m&m<=U,my(ell=(m^2-n/m)/3);if(denominator(ell)==1&&issquare(m^2-4*ell),return(1))));0 \\ _Charles R Greathouse IV_, Apr 16 2013

T=thueinit('z^3+1);
is(n)=n==0 || #select(v->min(v[1],v[2])>=0, thue(T,n))>0 \\ _Charles R Greathouse IV_, Nov 29 2014

a004999 n = a004999_list !! (n-1)
a004999_list = filter c2 [1..] where
   c2 x = any (== 1) $ map (a010057 . fromInteger) $
                       takeWhile (>= 0) $ map (x -) $ tail a000578_list
-- _Reinhard Zumkeller_, Dec 20 2013