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This paper discloses secrets and logics of the short formula of ancient Vedic Mathematics Yavadunam Tavadunikritya Varganicha Yojayet Sutra in finding the cube of a positive number. Through the formalization process, we have aimed to bridge the gap between ancient mathematical wisdom and modern theoretical foundations, showcasing the timeless utility of Vedic techniques in mathematical calculations. The sutra has been reviewed using the algebraic explanation in terms of decimal number system of the multiplication process by applying Binomial theorem for the positive integral exponent 3. Some more short-cut techniques have been discussed to explain the sutra and it has been found that they are producing the same result. There are shortcomings that have been found in applying the sutra, which has been solved using some other techniques as a special rule. Later the sutra has been discussed for negative integers also with a note. Before coming to the conclusion, we have discussed some limitations of the sutra, although that has been solved in the paper but with a different process. We have discussed the implications of the sutra for modern computational methods and educational practices, suggesting potential areas for further research.