Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
from collections import deque


def main():
    N = int(input())

    cnt_all = deque([])
    for n in range(1, N + 1):
        cnt = 0

        for x in range(1, 101):
            for y in range(1, 101):
                for z in range(1, 101):
                    ans = x ** 2 + y ** 2 + z ** 2 + x*y + y*z + z*x
                    if ans == n:
                        cnt += 1
                    elif ans > n:
                        break
        # ---------
        cnt_all.append(str(cnt))

    print("\n".join(cnt_all))

if __name__ == "__main__":
    main()


Fixed submission:
from collections import deque


def main():
    N = int(input())
    arr = deque(['0','0','0','0','0','1','0','0','0','0','3','0','0','0','0','0','3','3','0','0','0','0','0','1','6','0','3','0','0','0','0','0','3','3','6','0','0','3','0','0','0','0','3','3','6','0','6','0','0','0','3','0','0','1','6','0','6','6','0','0','6','0','0','0','0','3','3','3','6','0','6','3','6','0','0','0','6','0','0','0','3','3','9','0','6','3','6','0','3','6','0','0','0','0','6','1','6','0','6','6','0','3','12','0','6','0','0','3','6','0','0','0','3','3','12','0','6','3','6','0','3','6','9','0','6','0','0','0','3','6','3','3','6','0','6','3','12','0','3','6','6','0','6','0','6','3','6','0','0','1','6','3','12','6','0','0','12','0','6','0','6','6','12','0','0','6','0','0','6','0','12','3','6','0','6','3','9','6','3','6','6','0','6','0','6','0','15','6','0','0','6','0','3','3','12','0','12','6','6','0','3','6','6','3','12','0','6','0','9','6','0','0','6','3','12','1','6','6','6','6','0','0','18','0','12','0','3','6','12','0','0','6','3','6','12','0','12','0','0','0','9','3','9','6','12','3','12','0','3','6','6','0','12','0','12','0','9','9','0','0','6','3','6','3','12','6','9','3','6','0','12','3','6','3','9','6','12','6','6','0','6','0','9','6','6','0','12','3','6','0','9','6','6','1','6','0','21','12','6','0','12','0','12','0','0','6','15','6','0','6','12','0','12','0','12','0','0','0','12','0','12','12','3','3','18','3','6','3','6','6','9','9','18','0','6','0','12','0','9','6','0','3','12','3','6','6','12','6','6','0','0','0','15','3','18','3','18','3','12','6','3','6','9','0','12','0','12','0','18','12','0','0','12','3','6','0','6','6','9','6','0','0','18','1','18','3','12','6','6','6','12','0','15','6','12','6','18','0','0','6','0','9','12','0','18','0','6','3','12','0','12','12','0','0','12','0','3','6','12','6','18','9','18','0','9','6','18','0','6','0','6','3','27','6','6','6','6','3','6','0','12','6','9','0','6','0','18','0','9','9','15','3','12','6','6','3','9','6','12','12','18','0','18','0','6','6','21','6','0','0','6','3','15','6','12','6','18','0','0','0','12','6','6','3','6','4','18','6','12','6','3','9','30','0','18','0','6','6','12','6','6','9','12','0','18','6','18','0','6','0','12','0','6','12','6','3','18','0','6','6','6','6','15','3','24','0','6','3','18','0','12','6','12','6','24','0','15','18','9','6','0','0','18','3','6','0','15','12','12','6','6','0','18','0','6','3','12','0','12','6','6','9','9','6','24','3','24','0','9','12','6','6','12','0','12','0','21','9','15','6','12','3','18','3','12','6','12','6','0','0','12','0','12','6','24','0','6','12','6','1','9','6','12','6','24','0','18','3','12','6','6','12','24','0','12','6','15','6','18','0','18','0','0','0','18','9','21','12','0','6','18','0','9','6','6','6','12','0','12','0','9','9','27','6','6','3','18','6','21','6','6','12','12','0','12','0','24','12','0','0','24','3','24','6','12','12','18','0','0','0','12','0','18','3','15','6','12','9','6','0','15','6','9','12','24','0','12','3','6','6','21','6','18','3','18','0','21','12','15','6','6','0','12','3','12','9','18','9','12','6','6','6','24','0','18','3','24','0','6','6','0','6','9','6','6','4','30','0','18','12','9','6','24','0','18','0','9','12','21','6','6','12','12','0','18','0','21','15','12','0','12','6','12','12','18','0','18','0','6','0','9','12','18','6','30','0','0','0','24','6','9','3','12','6','30','3','6','12','6','12','12','0','36','0','6','3','27','12','12','6','6','6','24','0','12','6','12','0','18','0','18','15','18','3','18','6','12','6','6','12','3','6','6','0','12','3','39','3','12','12','12','3','18','0','21','12','21','6','18','0','12','0','9','9','12','9','24','9','12','6','12','6','33','0','6','0','18','0','9','15','12','6','24','6','6','3','15','6','15','12','18','0','18','1','18','6','12','6','6','0','24','6','24','12','18','6','24','0','6','6','12','15','24','0','24','6','6','0','18','0','15','18','12','0','24','0','12','6','12','12','18','6','24','0','0','6','24','3','12','0','12','6','30','9','6','12','24','12','12','0','15','18','12','0','18','0','24','6','15','6','18','3','18','3','12','6','24','12','12','12','6','0','36','0','18','3','6','12','6','9','12','0','3','12','36','0','30','0','12','0','18','6','12','9','12','6','24','3','18','12','15','9','24','0','18','6','18','9','18','12','6','6','24','3','24','0','12','12','12','0','6','0','27','12','18','3','30','3','18','6','0','12','15','6','18','0','24','0','9','6','9','12','18','7','24','0','24','12','15','12','24','0','24','0','6','9','30','9','6','6','0','9','33','12','36','0','12','0','18','0','6','21','12','6','36','6','0','3','18','6','12','6','24','0','12','3','24','6','9','12','6','6','30','6','18','12','9','9','12','0','30','3','18','3','27','6','30','12','12','0','24','0','27','12','6','0','24','3','18','18','9','6','18','0','12','3','33','18','12','9','6','0','12','6','30','0','24','12','12','0','30','6','6','6','0','6','24','0','12','0','18','15','33','6','30','15','18','0','9','12','24','9','12','0','18','6','27','18','15','6','18','3','24','0','6','6','36','12','18','0','12','3'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    for n in range(1, N + 1):
        print(arr.popleft())
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3


def main():
    N = int(input())

    for n in range(1, N + 1):
        cnt = 0

        for x in range(1, 101):
            for y in range(1, 101):
                for z in range(1, 101):
                    ans = x ** 2 + y ** 2 + z ** 2 + x*y + y*z + z*x
                    if ans == n:
                        cnt += 1
                    elif ans > n:
                        break
        # ---------
        print(cnt)


if __name__ == "__main__":
    main()


Fixed submission:
from collections import deque


def main():
    N = int(input())
    arr = 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    for n in range(1, N + 1):
        print(arr.popleft())
if __name__ == "__main__":
    main()