Cube of a natural number

Write the cubes of 5 natural numbers of the form 3n+2(ie.5,8,11,) and verify the following: The cube of a natural number of the form 3n+2 is a natural number of the same form 3n+2 is a natural number of the same form i.e.when it is dividend by 3the remainder is 2

Write the cubes of 5 natural number which are of form 3n+1(edot 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 3n+1 is a natural number of the same form i.e.when divided by 3 it leaves the remainder 1

Write the cubes of 5 natural numbers of which are multiples of 7 and verify the following The cube of multiple of 7 is a multiple of 7^(3)

a, b, c are positive integers froming an increasing G.P . whose common ratio is rational number, b - a is cube of natural number and log_(6)a + log_(6)b + log_(6)c = 6 then a + b + c is divisible by

How many natural numbers are there with the property that they can be expressed as the sum of the cubes of two natural numbers in two different ways.

Which of the following are cubes of odd natural numbers? 125,343,1728,4096,327686859