Buggy python submission (verdict: Runtime Error):
#!/usr/bin/python
# -*- coding: UTF-8 -*-

import math
import sys


def calc_p(a, b, c):
    u = {a, b, c}
    if len(u) == 3:
        return 6
    if len(u) == 2:
        return 3
    if len(u) == 1:
        return 1
    else:
        raise


def std_in():
    return sys.stdin.readline().strip()


def _main():
    N = int(std_in())
    fn = [0] * (N + 1)
    x_max = int(math.sqrt(N - 2)) - 1

    n2 = [i**2 for i in range(1, x_max + 1)]

    ij = [[0 for _ in range(1, x_max + 1)] for _ in range(1, x_max + 1)]
    for i in range(x_max):
        for j in range(i, x_max):
            ij[i][j] = (i+1) * (j+1)

    for x in range(1, x_max + 1):
        y_min = x
        x2 = n2[x-1]
        for y in range(y_min, x_max + 1):
            z_min = y
            y2 = n2[y-1]
            xy = ij[x-1][y-1]
            tmp_n = x2 + xy + y2
            if tmp_n > N:
                break
            for z in range(z_min, x_max + 1):
                z2 = n2[z-1]
                yz = ij[y-1][z-1]
                zx = ij[x-1][z-1]
                n = tmp_n + z2 + yz + zx
                if n > N:
                    break
                fn[n] += calc_p(x, y, z)

    for i in range(1, N + 1):
        print(fn[i])


if __name__ == "__main__":
    _main()


Fixed submission:
#!/usr/bin/python
# -*- coding: UTF-8 -*-

import math
import sys


def calc_p(a, b, c):
    u = {a, b, c}
    if len(u) == 3:
        return 6
    if len(u) == 2:
        return 3
    if len(u) == 1:
        return 1
    else:
        raise


def std_in():
    return sys.stdin.readline().strip()


def _main():
    N = int(std_in())
    fn = [0] * (N + 1)
    if N == 1:
        x_max = 1
    else:
        x_max = int(math.sqrt(N - 2)) - 1

    n2 = [i**2 for i in range(1, x_max + 1)]

    ij = [[0 for _ in range(1, x_max + 1)] for _ in range(1, x_max + 1)]
    for i in range(x_max):
        for j in range(i, x_max):
            ij[i][j] = (i+1) * (j+1)

    for x in range(1, x_max + 1):
        y_min = x
        x2 = n2[x-1]
        for y in range(y_min, x_max + 1):
            z_min = y
            y2 = n2[y-1]
            xy = ij[x-1][y-1]
            tmp_n = x2 + xy + y2
            if tmp_n > N:
                break
            for z in range(z_min, x_max + 1):
                z2 = n2[z-1]
                yz = ij[y-1][z-1]
                zx = ij[x-1][z-1]
                n = tmp_n + z2 + yz + zx
                if n > N:
                    break
                fn[n] += calc_p(x, y, z)

    for i in range(1, N + 1):
        print(fn[i])


if __name__ == "__main__":
    _main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/python
# -*- coding: UTF-8 -*-

import sys
import math


def input():
    return sys.stdin.readline().strip()


def main():
    N = int(input())
    x_max = int(math.sqrt(N - 2))
    fN = [0] * N
    n2 = [i**2 for i in range(1, N + 1)]
    ij = [[0] * (N+1) for _ in range(N+1)]

    for i in range(1, N+1):
        for j in range(i, N+1):
            ij[i][j] = i * j

    for i in range(N):
        for x in range(1, x_max):
            y_min = x
            x2 = n2[x]
            for y in range(y_min, x_max):
                z_min = y
                y2 = n2[y]
                xy = ij[x][y]
                if x2 + y2 + xy > N:
                    break
                for z in range(z_min, x_max):
                    if x2 + y2 + n2[z] + xy + ij[y][z] + ij[z][x] > N:
                        break
                    if x2 + y2 + n2[z] + xy + ij[y][z] + ij[z][x] == N:
                        fN[i] += 1

    for n in fN:
        print(n)


if __name__ == "__main__":
    main()


Fixed submission:
#!/usr/bin/python
# -*- coding: UTF-8 -*-

import math
import sys


def calc_p(a, b, c):
    u = {a, b, c}
    if len(u) == 3:
        return 6
    if len(u) == 2:
        return 3
    if len(u) == 1:
        return 1
    else:
        raise


def std_in():
    return sys.stdin.readline().strip()


def _main():
    N = int(std_in())
    fn = [0] * (N + 1)
    if N == 1:
        x_max = 1
    else:
        x_max = int(math.sqrt(N - 2)) - 1

    n2 = [i**2 for i in range(1, x_max + 1)]

    ij = [[0 for _ in range(1, x_max + 1)] for _ in range(1, x_max + 1)]
    for i in range(x_max):
        for j in range(i, x_max):
            ij[i][j] = (i+1) * (j+1)

    for x in range(1, x_max + 1):
        y_min = x
        x2 = n2[x-1]
        for y in range(y_min, x_max + 1):
            z_min = y
            y2 = n2[y-1]
            xy = ij[x-1][y-1]
            tmp_n = x2 + xy + y2
            if tmp_n > N:
                break
            for z in range(z_min, x_max + 1):
                z2 = n2[z-1]
                yz = ij[y-1][z-1]
                zx = ij[x-1][z-1]
                n = tmp_n + z2 + yz + zx
                if n > N:
                    break
                fn[n] += calc_p(x, y, z)

    for i in range(1, N + 1):
        print(fn[i])


if __name__ == "__main__":
    _main()