A Modish Glance of Integer Solutions to Non-homogeneous Cubic Diophantine Equation with Three Unknowns 7 (x2-xy+y2)= 12 z3

The main thrust of this paper is focused on determining varieties of non-zero distinct integer solutions to the non-homogeneous ternary cubic Diophantine  equation 7 (x²-xy+y²)= 12 z³ . Various choices of integer solutions to the above equation are obtained by reducing it to the equation which is solvable, through employing suitable transformations and applying the factorization method.