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The aim of this paper is to present a comprehensive survey of cubic Fibonacciidentities, trying to uncover as many as possible. From the outset, ourrationale for a very careful search on an apparently obscure problem was notonly a matter of mathematical curiosity, but also motivated by a quest for 3DFibonacci spirals. As we were not able to find any survey on the particulartopic of cubic Fibonacci identities we decided to try to fill this void. Westarted by surveying many Fibonacci identities and recording cubic ones.Obviously, tracing all Fibonacci identities (for identifying a handful) is adaunting task. Checking several hundred we have realized that it is not alwaysclear who the author is. The reason is that in many cases an identity wasstated in one article (sometimes without a proof, e.g., as an open problem, ora conjecture) while later being proven in another article, or effectivelyrediscovered independently by other authors. However, we have done our best topresent the identities chronologically. We have supplied our own proof for oneidentity, having tried, but failed, to find a published proof. For all theother identities, we either proved them on a computer, or else verified by handtheir original published proofs. Somehow unexpectedly, our investigations haverevealed only a rather small number of cubic Fibonacci identities, representinga tiny fraction of all published Fibonacci identities (most of which are linearor quadratic). Finally, out of these, only a handful of cubic Fibonacciidentities are homogeneous.

Survey of Cubic Fibonacci Identities - When Cuboids Carry Weight