# Cube Sum Pairs

Posted: 29 Dec, 2020
Difficulty: Easy

## PROBLEM STATEMENT

#### You are given a positive integer N, and you have to find the number of ways to represent N as a sum of cubes of two integers(let’s say A and B), such that:

``````N = A^3 + B^3.
``````

#### Note:

``````1. A should be greater than or equal to one (A>=1).
2. B should be greater than or equal to zero (B>=0).
3. (A, B) and (B, A) should be considered different solutions, if A is not equal to B, i.e (A, B) and (B, A) will not be distinct if A=B.
``````
##### Input Format:
``````The first line of the input contains an integer T denoting the number of test cases.

The first and only line of each test case consists of a single positive integer N.
``````
##### Output Format:
``````For each test case, print an integer that denotes the count of the number of ways of representing N as a sum of cubes of 2 integers (A and B) in a separate line.
``````
##### Note:
``````You don't have to print anything, it has already been taken care of. Just Implement the given function.
``````
##### Constraints:
``````1 <= T <= 10^3
1 <= N <= 10^8
Time Limit: 1 sec.
`````` Approach 1
1. Maintain a counter which will count possible pairs (A, B).
2. Iterate over all possible ‘A’ values.
• Possible ‘A’ values are in the range 1 to N.
3. For each ‘A’ value iterate over all possible values of ‘B’
• Possible ‘B’ values are in the range 0 to N.
4. If ‘A’^3 + ‘B’^3 comes to be N, then increment the counter.