This paper aims to develop an elegant formula for the series of consecutive cubes of natural numbers under alternating signs. In addition, this paper investigates the formula under odd and even number of terms and discuss some important findings.

This paper aims to construct a new formula that generates a generalized version of congruent numbers based on a generalized version of Pythagorean triples. Here, an elliptic curve equation is constructed from the derived generalized version of Pythagorean triples and congruent numbers and gives some new results.