Answer:
We can use the identity, a³ + b³ = (a +b)(a² - ab + b²)
[tex]\sf a^6 + \dfrac{1}{8}=(a^2)^3 + \left(\dfrac{1}{2}\right)^3[/tex]
[tex]\sf = (a^2 + \dfrac{1}{2})((a^2)^2+ a^2*\dfrac{1}{2}+(\dfrac{1}{2})^2)\\\\\\=(a^2+\dfrac{1}{2})(a^4+\dfrac{a^2}{2}+\dfrac{1}{4})[/tex]
