Write cubes of 5 natural numbers which are of the form 3n+1 (e.g 4, 7, 10, ...) and verify the following: 'The cube of a natural number of the form 3n +1 is a natural number of the same form'.

The 5 natural numbers which are of the form 3n + 1 (e.g 4, 7, 10, …) are as follows:
3 ൱ + 1 = 3 + 1 = 4
3 ൲ + 1 = 6 + 1 = 7
3 ൳ + 1 = 9 + 1 = 10
3 ൴ + 1 = 12 + 1 = 13
3 ൵ + 1 = 15 + 1 = 16
The cubes of 5 natural numbers which are of the form 3n + 1 (e.g 4, 7, 10, …) are as follows:
(4)³ = 4 × 4 ൴ = 64
(7)³ = 7 ൷ ൷ = 343
(10)³ = 10 휐 휐 = 1000
(13)³ = 13 휓 휓 = 2197
(16)³ = 16 × 16 × 16 = 4096
Verification:
64 = 3 × 21 + 1
343 = 3 × 114 + 1
1000 = 3 × 333 + 1
2197 = 3 × 732 + 1
4096 = 3 × 1365 + 1
.^.. 'The cube of a natural number of the form 3n +1 is a natural number of the same form'.