Sum of squares of Fibonacci numbers

Statement

The identity $F_1^2+F_2^2+\dots+F_n^2=F_n\,F_{n+1}$ holds. Compute $F_1^2+\dots+F_7^2$.

Solution

The first seven Fibonacci numbers are $1,1,2,3,5,8,13$. The sum of squares: $1+1+4+9+25+64+169=\boxed{273}.$ Matching the identity, $F_7\,F_8=13\cdot 21=273$.