Sum of squares of Fibonacci numbers

Given a positive integer N. The task is to find the sum of squares of all Fibonacci numbers up to N-th Fibonacci number. That is, 
 

f02 + f12 + f22+.......+fn2 

where fi indicates i-th fibonacci number.

Fibonacci numbers: f₀=0 and f₁=1 and f_i=f_i-1 + f_i-2 for all i>=2.
Examples: 
 

Input: N = 3
Output: 6
Explanation: 0 + 1 + 1 + 4 = 6

Input: N = 6
Output: 104
Explanation: 0 + 1 + 1 + 4 + 9 + 25 + 64 = 104

Method 1: Find all Fibonacci numbers till N and add up their squares. This method will take O(n) time complexity.
Below is the implementation of this approach: 
 

Sum of squares of Fibonacci numbers is : 104

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

Method 2: We know that for i-th Fibonacci number,
 

fi+1 = fi + fi-1 for all i>0

Or, fi = fi+1 - fi-1 for all i>0
Or, fi2 = fifi+1 - fi-1fi

So for any n>0 we see,
 

f₀² + f₁² + f₂²+.......+f_n² 
= f₀² + ( f₁f₂- f₀f₁)+(f₂f₃ - f₁f₂ ) +.............+ (f_nf_n+1 - f_n-1f_n ) 
= f_nf_n+1 (Since f₀ = 0) 
 

This identity also satisfies for n=0 (For n=0, f₀² = 0 = f₀ f₁).
Therefore, to find the sum, it is only needed to find f_n and f_n+1. To find f_n in O (log n) time. Refer to Method 5 or method 6 of this article.
Below is the implementation of the above approach: 
 

Sum of Squares of Fibonacci numbers is : 104

Time Complexity: O(logn)
Auxiliary Space: O(n)