Taxicab Numbers

A taxicab number is a positive integer that can be expressed as the sum of two positive cubes in more than one way.¹

Implement the function

val taxicab : int -> int

so that taxicab n is the number of ways n can be expressed as the sum of two positive cubes. The behavior of the function is undefined if n is not positive.

let _ = assert (taxicab 2 = 1)
let _ = assert (taxicab 5 = 0)
let _ = assert (taxicab 1729 = 2)  (* 1729 = 1^3 + 12^3 = 3^3 + 9^3 *)
let _ = assert (taxicab 4104 = 2)  (* 4104 = 2^3 + 16^3 = 9^3 + 15^3 *)