This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
30429 is a term because 30429 = 1^3 + 4^3 + 7^3 + 30^3 = 1^3 + 16^3 + 17^3 + 26^3 = 2^3 + 12^3 + 21^3 + 25^3 = 3^3 + 3^3 + 14^3 + 29^3 = 4^3 + 17^3 + 21^3 + 23^3 = 5^3 + 11^3 + 15^3 + 28^3 = 6^3 + 6^3 + 22^3 + 25^3 = 7^3 + 14^3 + 18^3 + 26^3.
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 8])
for x in range(len(rets)):
print(rets[x])
N:= 1000: # for terms <= N
B:= Vector(N):
for i from 1 while 4*i^2 <= N do
for j from i while i^2 + 3*j^2 <= N do
for k from j while i^2 + j^2 + 2*k^2 <= N do
for l from k do
m:= i^2 + j^2 + k^2 + l^2;
if m > N then break fi;
B[m]:= B[m]+1
od od od od:
select(t -> B[t] >= 7, [$1..N]); # Robert Israel, Oct 23 2020