Sum of square of first n even numbers Last Updated : 22 Sep, 2022 Comments Improve Suggest changes Like Article Like Report Try it on GfG Practice Given a number n, find sum of square of first n even natural numbers. Examples: Input : 3Output : 56 22 + 42 + 62 = 56 Input : 8Output : 81622 + 42 + 62 + 82 + 102 + 122 + 142 + 162 = 816 Recommended PracticePower of Pow | Even NumberTry It! A simple solution is to traverse through n even numbers and find the sum of square. C++ // Simple C++ method to find sum // of square of first n even numbers. #include <iostream> using namespace std; int squareSum(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum += (2 * i) * (2 * i); return sum; } // Driver Code int main() { cout << squareSum(8); return 0; } Java // Simple Java method to find sum of // square of first n even numbers. import java.io.*; class GFG { static int squareSum(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum += (2 * i) * (2 * i); return sum; } // Driver Code public static void main(String args[]) throws IOException { System.out.println(squareSum(8)); } } // This code is contributed by Nikita Tiwari Python3 # Simple Python3 code to # find sum of square of # first n even numbers def squareSum( n ): sum = 0 for i in range (0, n + 1): sum += (2 * i) * (2 * i) return sum # driver code ans = squareSum(8) print (ans) # This code is contributed by Saloni Gupta C# // Simple C# method to find sum of // square of first n even numbers. using System; class GFG { static int squareSum(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum += (2 * i) * (2 * i); return sum; } // Driver code public static void Main() { Console.Write(squareSum(8)); } } // This code is contributed by vt_m. PHP <?php // Simple PHP method to find sum of // square of first n even numbers. function squareSum($n) { $sum = 0; for ($i = 1; $i <= $n; $i++) $sum += (2 * $i) * (2 * $i); return $sum; } echo squareSum(8); // This code is contributed by vt_m. ?> JavaScript <script> // Simple Javascript method to find sum // of square of first n even numbers. function squareSum(n) { sum = 0; for(let i = 1; i <= n; i++) sum += (2 * i) * (2 * i); return sum; } // Driver Code document.write(squareSum(8)); // This code is contributed by souravmahato348 </script> Output: 816 Time Complexity: O(n), where n represents the given integer.Auxiliary Space: O(1), no extra space is required, so it is a constant. An efficient solution is to apply below formula. sum = 2 * n * (n + 1) * (2 * n + 1)/3 How does it work? We know that sum of square of first n natural numbers is = n(n+1)/2 Sum of square of first n even natural numbers = 22 + 42 + .... + (2n)2 = 4 * (12 + 22 + .... + n2) = 4 * n(n+1)(2n+1) / 6 = 2 * n(n+1)(2n+1)/3 C++ // Efficient C++ method to find sum // of square of first n even numbers. #include <iostream> using namespace std; int squareSum(int n) { return 2 * n * (n + 1) * (2 * n + 1) / 3; } // Driver code int main() { cout << squareSum(8); return 0; } Java // Efficient Java method to find sum // of square of first n even numbers. import java.io.*; class GFG { static int squareSum(int n) { return 2 * n * (n + 1) * (2 * n + 1) / 3; } // Driver Code public static void main(String args[]) throws IOException { System.out.println(squareSum(8)); } } // This code is contributed by Nikita Tiwari Python3 # Efficient Python3 code to # find sum of square of # first n even numbers def squareSum( n ): return int(2 * n * (n + 1) * (2 * n + 1) / 3) # driver code ans = squareSum(8) print (ans) # This code is contributed by Saloni Gupta C# // Efficient C# method to find sum // of square of first n even numbers. using System; class GFG { static int squareSum(int n) { return 2 * n * (n + 1) * (2 * n + 1) / 3; } // driver code public static void Main() { Console.Write(squareSum(8)); } } // This code is contributed by vt_m. PHP <?php // Efficient PHP method to find sum of // square of first n even numbers. function squareSum( $n) { return 2 * $n * ($n + 1) * (2 * $n + 1) / 3; } echo squareSum(8); // This code is contributed by vt_m. ?> JavaScript <script> // JavaScript program to find sum of // square of first n even numbers. function squareSum(n) { let sum = 0; for (let i = 1; i <= n; i++) sum += (2 * i) * (2 * i); return sum; } // Driver code document.write(squareSum(8)); </script> Output : 816 Time complexity: O(1) since performing constant operationsAuxiliary Space: O(1) because constant extra space has been used Comment More infoAdvertise with us Next Article Analysis of Algorithms D dharmendra_kumar Follow Improve Article Tags : Misc Mathematical DSA series number-theory Numbers series-sum +3 More Practice Tags : MathematicalMiscnumber-theoryNumbersseries +1 More Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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