Solutions to cubic equation have been explored extensively by mathematicians over the centuries. Different solutions have been devised for cubic equations most of which are able to solve reducible cubic equations and they usually involve trial and error procedures. 16th century mathematicians also devised solutions for irreducible cubic equations. One way of solving irreducible cubic equation usually involves the substitution  which reduces the given equation to the depressed form, ????3 = ???????? + ????. This actually raises the question as to how this substitution is obtained, and whether or not some deductive steps can prove it analytically. For long now, it has been inconceivable that the procedure deployed in the method of completing the square for quadratic equations can be extended to cubic equations. This study investigated the possibility of providing a general and more reliable method of finding the solutions to cubic equations by deploying the method of completing the cube. This method is not only an extension of the method of completing the square but also a proof of the substitution, . It 3???? shows just how this substitution is generated.