Sum of positive integral powers of first n natural numbers has been an interesting problem for many years. Mathematicians, students and research scholars have been attempting to crack this problem for decades. The primary objective of this talk is to generate a generalized result for an ancient interesting problem in the research field of Analytic Number Theory. That problem states that sum of kth powers of first n- natural number coincides with a unique a polynomial of degree (k+1) in n over natural numbers. The existence and uniqueness of this polynomial are established using the principles of Linear Algebra. The innovative result derived here opens a way to write the formula for the sum of any positive integral power of first n- natural numbers.