Can you prove that 8 is the largest cube in the Fibonacci sequence?



Is 8 the largest cube in the Fibonacci sequence?
For a much more accessible treatment, and history of the result, see [Andrejic (2006) "On Fibonacci powers"](http://www.doiserbia.nb.rs/img/doi/0353-8893/2006/0353-88930617038A.pdf)


