$\text{a)}w\left(x\right)=x^3-8=x^3-2^3=\left(x-2\right)\left(x^2+2x+4\right)$  

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$\text{b)}w\left(x\right)=x^3+64=x^3+4^3=\left(x+4\right)\left(x^2-4x+16\right)$  

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$\text{c)}w\left(x\right)=x^3-2=x^3-{\left(\sqrt[3]{2}\right)}^3=\left(x-\sqrt[3]{2}\right)\left(x^2+\sqrt[3]{2}x+\sqrt[3]{4}\right)$  

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$\text{d)}w\left(x\right)=x^3-16=x^3-{\left(\sqrt[3]{16}\right)}^3=x^3-{\left(2\sqrt[3]{2}\right)}^3=\left(x-2\sqrt[3]{2}\right)\left(x^2+2\sqrt[3]{2}x+4\sqrt[3]{4}\right)$