# Fibonacci Number equal to Sum of Sequence of Cubes

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## Contents

## 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.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $2584$