$$2\times \left( 3+1 \right)\times \left( {{3}^{2}}+1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)=$$． 
Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula
$$=\left( 3-1 \right)\times \left( 3+1 \right)\times \left( {{3}^{2}}+1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$=\left( {{3}^{2}}-1 \right)\times \left( {{3}^{2}}+1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$=\left( {{3}^{4}}-1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$=\cdots $$  $$=\left( {{3}^{32}}-1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$={{3}^{64}}-1$$． 