Question

Write cubes of all natural numbers between 1 and 20 and verify the following statement. If the statement is true then answer is $1$ if not then the answer is $0$

Statement: Cubes of all even natural numbers are even.

Answer 1

$1^3=1$

$2^3=8$

$3^3=27$

$4^3=64$

$5^3=125$ so on.

Assume a general even number to be of the form $2n$ where $n$ is a whole number.

This is true for all even numbers, by definition are divisible by 2.

Cube of a general even number= $2n\times 2n\times 2n=8n$

This number $8n$ is again divisible by 2

So cube of an even natural number is even.