Buggy python submission (verdict: Time Limit Exceeded):
import sys
print = sys.stdout.write

N = int(input())


for n in range(1, N+1):
    ans = 0
    for x in range(1, int(n**0.5 +1)):
        if x ** 2 >= n-4:
            break
        for y in range(x, int(n**0.5+1)):
            if x**2 + y**2 + x*y >= n-2:
                break
            for z in range(y, int(n**0.5+1)):
                if x**2 + y**2 + z**2 + x*y + y*z + z*x == n:
                    if x == y == z:
                        ans += 1
                    elif x == y or y == z:
                        ans += 3
                    else:
                        ans += 6
    print(str(ans) + '\n')


Fixed submission:
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48,
24,
36,
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54,
15,
108,
0,
84,
18]

n = int(input())
print('\n'.join(map(str, result[:n])))