This paper presents the development of cubature rules with reduced number of points that are capable of evaluating multi dimensional expectation integrals with respect to a Gaussian pdf. Alternatively this can be considered as an extension to the conventional 3rd order unscented transformation by satisfying higher order moment constraint equations. New sets of sigma points are defined to satisfy moment equations up to order 8. The proposed sigma points are shown to be efficient in terms of exactness while integrating polynomials and yet just employ a small fraction of the number of points used by the traditional Gaussian-Hermite Product rule. In the perspective of non-linear filtering, with an aide of a typical air traffic scenario, the new set of sigma points have been shown to provide a significant advantage in terms of accuracy and reduced computational complexity, thus providing a promising on-line execution.