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.
3663 = 1^3 + 10^3 + 11^3 + 11^3
= 2^3 + 4^3 + 6^3 + 15^3
= 2^3 + 9^3 + 9^3 + 13^3
= 4^3 + 7^3 + 8^3 + 14^3
so 3663 is a term.
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,4):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
print(rets[x])