Thanks to all.

@skeeter

Thanks for giving insight to the simplicity of the equation. I am known to over-think everything. Probably from a lack in confidence.

@All

From prior post I was able to deduce the solutions:

@Plato

This is what MathType generated when I copy and pasted the equation above(start and end tags contained math and /math):

[]\begin{array}{l}

a{}^3 - b{}^3 = (x - a)(x{}^2 + ax + a{}^2)\\

x{}^6 - 2x{}^3 + 1 = (x{}^3 - 1){}^2\\

(x - 1){}^2(x{}^2 + ( - 1)x + ( - 1){}^2){}^2\\

(x - 1){}^2(x{}^2 - x + 1){}^2

\end{array}[]

Then I edited the markup code and got:

$\displaystyle

\begin{array}{l}

a{}^3 - b{}^3 = (x - a)(x{}^2 + ax + a{}^2)\\

x{}^6 - 2x{}^3 + 1 = (x{}^3 - 1){}^2\\

(x - 1){}^2(x{}^2 + ( - 1)x + ( - 1){}^2){}^2\\

(x - 1){}^2(x{}^2 - x + 1){}^2

\end{array}

$