Verified answer

[tex]\displaystyle\bf\\1)\\\\\Big(\sqrt{2} -\sqrt{8} \Big)^{3} =\Big(\sqrt{2}-\sqrt{4\cdot 2}\Big)^{3} =\Big(\sqrt{2} -2\sqrt{2} \Big)^{3}=\Big(-\sqrt{2} \Big)^{3} =-2\sqrt{2} \\\\\\2)\\\\\Big(\sqrt{3} -\sqrt{12} \Big)^{3} =\Big(\sqrt{3}-\sqrt{4\cdot 3}\Big)^{3} =\Big(\sqrt{3} -2\sqrt{3} \Big)^{3}=\Big(-\sqrt{3} \Big)^{3} =-3\sqrt{3}[/tex]