# Fibonacci Number equal to Sum of Sequence of Cubes

## Theorem

The following Fibonacci number can be expressed as the sum of a sequence of cubes:

$F_{18} = 2584 = 7^3 + 8^3 + 9^3 + 10^3$

## Proof

 $\displaystyle 2584$ $=$ $\displaystyle 343 + 512 + 729 + 1000$ $\displaystyle$ $=$ $\displaystyle 7^3 + 8^3 + 9^3 + 10^3$

$\blacksquare$

## Historical Note

In his Curious and Interesting Numbers, 2nd ed. of $1997$, David Wells attributes this result to Michal Stajsczak, but gives no context.