Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())

n=1
while n<=N:
  ans=0
  x=1
  while x*x<n:
    y=1
    while x*x+y*y+x*y<=n:
      z=1
      while x*x+y*y+z*z+x*y+y*z+z*x<=n:
        if x*x+y*y+z*z+x*y+y*z+z*x==n:
          ans+=1
        z+=1
      y+=1
    x+=1
  print(ans)
  n+=1

Fixed submission:
f=[0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,0,3,3,0,0,0,0,0,1,6,0,3,0,0,0,0,0,3,3,6,0,0,3,0,0,0,0,3,3,6,0,6,0,0,0,3,0,0,1,6,0,6,6,0,0,6,0,0,0,0,3,3,3,6,0,6,3,6,0,0,0,6,0,0,0,3,3,9,0,6,3,6,0,3,6,0,0,0,0,6,1,6,0,6,6,0,3,12,0,6,0,0,3,6,0,0,0,3,3,12,0,6,3,6,0,3,6,9,0,6,0,0,0,3,6,3,3,6,0,6,3,12,0,3,6,6,0,6,0,6,3,6,0,0,1,6,3,12,6,0,0,12,0,6,0,6,6,12,0,0,6,0,0,6,0,12,3,6,0,6,3,9,6,3,6,6,0,6,0,6,0,15,6,0,0,6,0,3,3,12,0,12,6,6,0,3,6,6,3,12,0,6,0,9,6,0,0,6,3,12,1,6,6,6,6,0,0,18,0,12,0,3,6,12,0,0,6,3,6,12,0,12,0,0,0,9,3,9,6,12,3,12,0,3,6,6,0,12,0,12,0,9,9,0,0,6,3,6,3,12,6,9,3,6,0,12,3,6,3,9,6,12,6,6,0,6,0,9,6,6,0,12,3,6,0,9,6,6,1,6,0,21,12,6,0,12,0,12,0,0,6,15,6,0,6,12,0,12,0,12,0,0,0,12,0,12,12,3,3,18,3,6,3,6,6,9,9,18,0,6,0,12,0,9,6,0,3,12,3,6,6,12,6,6,0,0,0,15,3,18,3,18,3,12,6,3,6,9,0,12,0,12,0,18,12,0,0,12,3,6,0,6,6,9,6,0,0,18,1,18,3,12,6,6,6,12,0,15,6,12,6,18,0,0,6,0,9,12,0,18,0,6,3,12,0,12,12,0,0,12,0,3,6,12,6,18,9,18,0,9,6,18,0,6,0,6,3,27,6,6,6,6,3,6,0,12,6,9,0,6,0,18,0,9,9,15,3,12,6,6,3,9,6,12,12,18,0,18,0,6,6,21,6,0,0,6,3,15,6,12,6,18,0,0,0,12,6,6,3,6,4,18,6,12,6,3,9,30,0,18,0,6,6,12,6,6,9,12,0,18,6,18,0,6,0,12,0,6,12,6,3,18,0,6,6,6,6,15,3,24,0,6,3,18,0,12,6,12,6,24,0,15,18,9,6,0,0,18,3,6,0,15,12,12,6,6,0,18,0,6,3,12,0,12,6,6,9,9,6,24,3,24,0,9,12,6,6,12,0,12,0,21,9,15,6,12,3,18,3,12,6,12,6,0,0,12,0,12,6,24,0,6,12,6,1,9,6,12,6,24,0,18,3,12,6,6,12,24,0,12,6,15,6,18,0,18,0,0,0,18,9,21,12,0,6,18,0,9,6,6,6,12,0,12,0,9,9,27,6,6,3,18,6,21,6,6,12,12,0,12,0,24,12,0,0,24,3,24,6,12,12,18,0,0,0,12,0,18,3,15,6,12,9,6,0,15,6,9,12,24,0,12,3,6,6,21,6,18,3,18,0,21,12,15,6,6,0,12,3,12,9,18,9,12,6,6,6,24,0,18,3,24,0,6,6,0,6,9,6,6,4,30,0,18,12,9,6,24,0,18,0,9,12,21,6,6,12,12,0,18,0,21,15,12,0,12,6,12,12,18,0,18,0,6,0,9,12,18,6,30,0,0,0,24,6,9,3,12,6,30,3,6,12,6,12,12,0,36,0,6,3,27,12,12,6,6,6,24,0,12,6,12,0,18,0,18,15,18,3,18,6,12,6,6,12,3,6,6,0,12,3,39,3,12,12,12,3,18,0,21,12,21,6,18,0,12,0,9,9,12,9,24,9,12,6,12,6,33,0,6,0,18,0,9,15,12,6,24,6,6,3,15,6,15,12,18,0,18,1,18,6,12,6,6,0,24,6,24,12,18,6,24,0,6,6,12,15,24,0,24,6,6,0,18,0,15,18,12,0,24,0,12,6,12,12,18,6,24,0,0,6,24,3,12,0,12,6,30,9,6,12,24,12,12,0,15,18,12,0,18,0,24,6,15,6,18,3,18,3,12,6,24,12,12,12,6,0,36,0,18,3,6,12,6,9,12,0,3,12,36,0,30,0,12,0,18,6,12,9,12,6,24,3,18,12,15,9,24,0,18,6,18,9,18,12,6,6,24,3,24,0,12,12,12,0,6,0,27,12,18,3,30,3,18,6,0,12,15,6,18,0,24,0,9,6,9,12,18,7,24,0,24,12,15,12,24,0,24,0,6,9,30,9,6,6,0,9,33,12,36,0,12,0,18,0,6,21,12,6,36,6,0,3,18,6,12,6,24,0,12,3,24,6,9,12,6,6,30,6,18,12,9,9,12,0,30,3,18,3,27,6,30,12,12,0,24,0,27,12,6,0,24,3,18,18,9,6,18,0,12,3,33,18,12,9,6,0,12,6,30,0,24,12,12,0,30,6,6,6,0,6,24,0,12,0,18,15,33,6,30,15,18,0,9,12,24,9,12,0,18,6,27,18,15,6,18,3,24,0,6,6,36,12,18,0,12,3,30,3,12,6,12,15,6,0,18,12,15,9,30,0,18,6,12,12,18,6,6,3,24,1,27,12,18,6,18,0,24,0,18,15,15,21,30,6,12,12,18,0,30,6,24,0,6,0,18,6,36,12,6,6,36,0,6,12,12,12,24,0,30,0,9,6,18,0,18,12,12,6,24,6,9,15,12,0,12,6,30,9,18,0,42,3,18,6,12,18,33,12,12,0,18,0,21,12,12,12,24,6,30,0,27,18,6,12,6,0,24,0,18,15,30,0,18,12,6,0,21,6,21,12,24,0,30,0,6,6,6,12,24,0,30,12,9,12,21,3,24,0,12,3,21,18,9,18,18,6,30,3,42,6,21,6,30,0,6,3,24,9,36,6,6,9,12,6,18,12,33,9,12,0,24,9,9,6,3,18,36,6,18,0,24,6,6,6,18,0,12,0,30,3,39,12,12,7,18,0,15,18,18,9,36,0,24,6,6,18,30,0,18,9,18,3,24,6,21,12,24,0,30,3,33,24,12,6,18,6,6,6,18,6,18,12,18,0,24,6,36,3,18,6,0,12,30,0,9,24,18,0,24,0,18,0,0,12,30,15,30,6,18,3,30,0,24,18,12,0,36,3,24,12,15,18,18,6,24,3,24,12,18,12,24,0,0,6,39,6,24,3,18,3,42,6,12,12,15,9,30,0,12,0,18,6,18,12,24,15,12,0,12,12,30,12,12,0,18,0,15,15,18,18,30,3,24,12,9,6,48,0,18,0,30,0,21,6,12,12,24,12,18,3,48,24,6,6,18,0,36,0,12,15,27,6,12,12,18,6,27,6,12,9,18,0,24,6,18,18,21,0,36,0,12,0,18,12,21,18,24,0,12,1,18,9,21,18,6,9,42,3,36,12,12,12,30,0,12,6,21,12,36,6,24,9,12,6,12,12,24,12,18,0,42,0,15,6,15,15,42,6,30,6,12,12,18,12,18,0,6,6,36,0,30,18,6,0,6,0,30,18,18,0,42,0,18,6,15,18,24,0,12,6,36,9,33,12,12,12,18,0,36,0,21,21,15,18,18,15,18,0,18,6,42,6,24,0,18,3,42,6,18,12,12,12,18,0,15,12,18,12,36,0,30,12,3,21,18,0,30,6,24,0,27,12,18,12,6,0,12,0,36,15,15,3,36,12,18,6,30,6,33,12,12,0,12,6,24,6,54,18,12,3,36,9,9,12,12,18,36,0,6,0,21,15,27,9,24,12,30,6,24,6,27,18,12,0,30,0,21,12,18,6,30,0,18,0,21,18,21,6,30,0,24,3,6,6,15,27,12,10,42,6,36,12,12,6,24,0,24,6,12,12,48,6,18,12,0,3,51,6,30,6,24,0,24,0,30,21,15,12,24,9,18,6,18,12,30,9,24,0,18,0,27,18,9,6,18,9,54,0,18,24,21,18,12,0,24,0,12,0,30,9,30,12,6,9,24,6,15,15,18,0,30,3,33,18,21,12,42,3,30,6,6,24,27,6,12,0,24,3,42,6,42,9,12,6,18,6,24,12,12,12,54,0,6,12,18,6,18,18,30,12,30,0,18,0,27,18,24,0,18,0,15,24,21,6,24,3,36,6,6,6,45,21,18,0,18,6,33,3,18,0,24,15,30,0,30,24,12,6,36,0,24,3,21,24,18,15,30,3,12,6,42,12,12,12,6,0,54,6,30,15,24,18,24,6,12,0,9,6,30,0,48,0,24,0,15,12,39,12,24,6,24,6,15,30,12,6,24,0,24,3,24,12,24,6,6,18,12,4,54,6,21,18,18,0,36,6,24,9,30,12,24,9,36,6,12,18,42,3,30,0,6,9,21,6,12,30,30,6,30,0,27,12,9,18,30,0,36,0,18,9,42,6,24,12,0,6,51,12,24,12,12,0,18,6,12,18,6,6,36,3,54,9,18,6,27,12,18,0,30,0,39,9,18,18,12,9,30,6,21,12,27,18,24,0,12,0,42,18,42,6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6,66,0,12,36,78,36,42,0,36,0,78,24,48,24,18,30,90,15,96,18,27,21,54,0,24,21,48,27,84,18,48,42,36,6,66,12,108,12,42,0,48,9,27,60,21,36,84,6,36,18,42,18,54,18,60,0,60,15,72,9,99,42,12,12,60,0,57,42,18,18,78,0,42,6,36,36,63,9,42,15,30,18,78,6,24,48,42,0,102,12,75,45,42,30,84,24,66,9,24,30,90,24,42,0,24,3,84,21,84,33,66,24,36,6,36,48,51,18,72,0,66,18,54,30,24,18,48,18,30,0,102,12,45,36,24,0,102,3,42,15,42,54,54,21,66,24,66,30,102,3,66,0,48,12,24,30,45,36,54,6,78,9,48,24,39,36,96,0,66,6,27,27,60,30,18,30,48,12,90,24,60,36,6,0,42,12,78,36,36,24,114,6,60,0,18,6,69,18,84,0,36,6,48,6,39,24,42,24,54,6,72,48,36,42,60,0,48,0,36,18,138,24,30,30,42,18,75,18,48,18,24,0,78,0,78,57,60,9,48,9,36,30,30,42,42,39,84,0,24,12,87,27,30,42,24,24,90,0,36,24,60,36,84,0,42,0,30,21,87,12,72,24,42,12,60,30,72,21,60,0,96,12,30,42,39,18,66,12,84,12,63,42,42,24,42,0,18,6,78,15,75,45,54,12,54,6,84,30,30,18,54,0,42,24,39,27,96,18,42,21,48,0,54,18,33,36,66,0,84,0,75,48,30,42,54,12,54,15,42,30,96,18,42,0,18,6,123,15,48,24,48,39,42,6,21,54,45,12,60,0,90,12,30,36,45,18,72,21,78,12,30,12,60,30,18,0,78,6,60,36,33,18,60,12,30,0,60,18,90,30,54,0,36,1,78,27,84,30,18,15,102,9,27,30,24,57,90,0,42,9,48,42,42,12,72,27,48,9,108,18,48,48,18,0,84,6,66,24,48,21,114,6,78,24,30,30,42,18,60,0,18,12,63,9,51,66,48,15,54,0,66,60,36,18,48,0,66,6,36,30,96,9,36,30,30,24,93,24,72,24,66,0,60,24,48,30,24,30,72,6,60,12,30,12,93,18,72,0,30,0,81,30,36,48,36,30,90,6,54,24,57,24,36,0,54,18,36,24,78,18,72,33,12,0,51,30,48,24,42,0,90,3,78,30,30,27,138,6,30,18,36,24,75,24,12,0,54,12,42,18,84,36,30,18,66,6,45,36,36,48,114,0,24,6,30,21,108,15,48,18,36,18,57,24,63,42,54,0,78,6,81,36,18,24,42,18,120,0,24,24,66,12,54,0,48,12,66,18,42,36,48,18,72,6,48,48,33,6,102,0,54,24,39,54,60,12,90,18,36,3,111,24,51,48,42,0,90,0,45,36,54,48,54,24,18,18,51,18,72,0,54,0,18,12,54,36,57,18,42,18,120,0,63,42,27,36,48,0,54,6,39,30,81,18,72,33,54,9,72,12,54,54,24,0,54,15,75,24,60,12,78,6,30,12,39,54,72,6,54,0,72,6,78,12,54,39,30,15,48,6,57,48,18,24,90,0,90,18,42,24,39,42,24,30,42,0,84,6,66,30,30,0,30,0,27,42,39,33,90,24,84,18,51,36,69,24,54,0,42,18,87,33,51,18,42,9,126,9,84,36,66,18,54,0,36,0,66,12,48,15,54,30,18,18,60,18,96,54,42,0,102,0,27,36,30,36,108,15,54,0,24,36,60,24,66,0,30,0,54,15,75,48,36,18,48,24,36,36,54,15,108,0,84,18]
N=int(input())
for i in range(N):
  print(f[i])