What are the remainders when a perfect cube is divided by 7?
13 ÷ 7 = 1
23 ÷ 7 = 1
33 ÷ 7 = 6
43 ÷ 7 = 1
53 ÷ 7 = 6
63 ÷ 7 = 6
73 ÷ 7 = 0
83 ÷ 7 = 1
93 ÷ 7 = 1
It can be observed that when a perfect cube is divided by 7, the remainders are 0, 1 or 6.