count_values.py

from collections import defaultdict


def product(a, b, c, d):
    return [(a, b, c, d), (a, b, d, c), (b, a, c, d), (b, a, d, c)]


def count_hack(n):
    results = []
    sums = defaultdict(set)
    for a in range(1, n):
        results.append((a, a, a, a))
        for b in range(a+1, n+1):
            results.extend(product(a, b, a, b))
            sum_ = a ** 3 + b ** 3
            for values in sums[sum_]:
                results += product(a, b, *values) + product(*values, a, b)
            sums[sum_].add((a, b))
    results.append((b, b, b, b))
    return results