Final answer:
To prove the statement, we can use the concept of prime factorization and the property that if a number is divisible by 2, then it is also divisible by all the powers of 2, including 8.
Step-by-step explanation:
To prove the statement: For every integer n, if n³ is divisible by 2, then n³ is divisible by 8, we can use the concept of prime factorization. Since 2 is a prime factor of 8, if n³ is divisible by 2, it means that n³ can be expressed as 2 multiplied by some other integers. To show that n³ is divisible by 8, we need to show that the other integers in the expression also have 2 as a factor. This can be done by using the property that if a number is divisible by 2, then it is also divisible by all the powers of 2, including 8.