Count cubes of size K inscribed in a cube of size N

Given two integers N and K, the task is to find the number of cubes of size K that can be contained in a cube of size N.

Examples:

Input: N = 2, K = 1
Output: 8
Explanation:
There are 8 cubes of size 1 that can be drawn inside the bigger cube of size 2. 

Input: N = 5, K = 2
Output: 64
Explanation:
There are 64 cubes of size 2 can be drawn inside the bigger cube of size 5.

Approach: The key observation to solve the problem is that the number of cubes inside the cube of size N is (N² * (N+1)²)/4. Therefore, the cubes of size K inside the cube of size N is:

Below is the implementation of the above approach:

C++

// C++ implementation of the
// above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the number
// of the cubes of the size K
int No_of_cubes(int N, int K)
{
    int No = 0;

    // Stores the number of cubes
    No = (N - K + 1);

    // Stores the number of cubes
    // of size k
    No = pow(No, 3);
    return No;
}

// Driver Code
int main()
{
    // Size of the bigger cube
    int N = 5;

    // Size of the smaller cube
    int K = 2;

    cout << No_of_cubes(N, K);
    return 0;
}

Java

// Java implementation of the
// above approach
class GFG{

// Function to find the number
// of the cubes of the size K
static int No_of_cubes(int N,
                       int K)
{
  int No = 0;

  // Stores the number of cubes
  No = (N - K + 1);

  // Stores the number of cubes
  // of size k
  No = (int) Math.pow(No, 3);
  return No;
}

// Driver Code
public static void main(String[] args)
{
  // Size of the bigger cube
  int N = 5;

  // Size of the smaller cube
  int K = 2;

  System.out.print(No_of_cubes(N, K));
}
}

// This code is contributed by Princi Singh

Python3

# Python3 implementation of the
# above approach

# Function to find the number
# of the cubes of the size K
def No_of_cubes(N, K):

    No = 0

    # Stores the number of cubes
    No = (N - K + 1)

    # Stores the number of cubes
    # of size k
    No = pow(No, 3)
    return No

# Driver Code

# Size of the bigger cube
N = 5

# Size of the smaller cube
K = 2

print(No_of_cubes(N, K))

# This code is contributed by sanjoy_62

C#

// C# implementation of the
// above approach
using System;

class GFG{

// Function to find the number
// of the cubes of the size K
static int No_of_cubes(int N, int K)
{
    int No = 0;

    // Stores the number of cubes
    No = (N - K + 1);

    // Stores the number of cubes
    // of size k
    No = (int)Math.Pow(No, 3);
    return No;
}

// Driver Code
public static void Main()
{

    // Size of the bigger cube
    int N = 5;

    // Size of the smaller cube
    int K = 2;

    Console.Write(No_of_cubes(N, K));
}
}

// This code is contributed by sanjoy_62

Javascript

<script>

// JavaScript program for
// the above approach

// Function to find the number
// of the cubes of the size K
function No_of_cubes(N, K)
{
  let No = 0;

  // Stores the number of cubes
  No = (N - K + 1);

  // Stores the number of cubes
  // of size k
  No = Math.pow(No, 3);
  return No;
}

// Driver code

  // Size of the bigger cube
  let N = 5;

  // Size of the smaller cube
  let K = 2;
  document.write(No_of_cubes(N, K));

  // This code is contributed by splevel62.
</script>

Output:

64

Time Complexity: O(1) 
Auxiliary Space: O(1)