Survey of Cubic Fibonacci Identities When Cuboids Carry Weight

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