The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$. It is known that $\sum_{k=1}^n F_k = F_{n+2} - 1$. What is $\sum_{k=1}^8 F_k$?