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# Prove that the cube of any integer can be written as the difference of two squares

**Chapter 1, Problem 1.4**

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**QUESTION:**

Prove that the cube of any integer can be written as the difference of two squares. [Hint:Notice thatn3 = (13 + 23 + + n3) - (13 + 23 + + (n - 1)3). ]

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### Questions & Answers

**QUESTION:**

Prove that the cube of any integer can be written as the difference of two squares. [Hint:Notice thatn3 = (13 + 23 + + n3) - (13 + 23 + + (n - 1)3). ]

**ANSWER:**

Step 1 of 4

Let us consider a is any integer.

Claim that , where p and q are any integers.

Consider and add, subtract the number in we get

As we know that,

By using above formula calculate, we have

Similarly, calculate