Is there a relation in geometry in which the third power of a segment is a function of other segments of a triangle?

Question

All the equations in geometry between segments are related to area or line or are nondimensional relations related to trigonometry.Is there a relation in geometry in which the third power of a segment is a function of other segments of a triangle?

Answer 1

Assuming that the "segments" of a triangle are the sides: If I'm understanding the question you're asking whether there exists a function $f$ such that if $A,B,C$ are the sides of a triangle then $$A^3=f(B,C).$$

The answer is obviously no. Has nothing to do with constructibility, as suggested in a comment. Consider a triangle with sides $A,B,C$ and another triangle with sides $A',B,C$, with $A'\ne A$.