Fibonacci Number equal to Sum of Sequence of Cubes

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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