How many perfect cubes you can find from 1 to 100? How many from −100 to 100?
13 = 1
23 = 8
33 = 27
43 = 64
Thus, there are 4 cubes from 1 to 100.
Now, 03 = 0
(−1)3 = −1
(−2)3 = −8
(−3)3 = −27
(−4)3 = −64
Hence, there are 9 cubes from −100 to 100.