$\text{The smallest integer larger than (}\sqrt{3}+\sqrt{2}{)}^{6 }is$

${\text{(}\sqrt{3}+\sqrt{2})}^6+{(\sqrt{3}-\sqrt{2})}^6$

$=2(6c_0{\left(\sqrt{3}\right)}^6+6_{c_2}{\left(\sqrt{3}\right)}^4{\left(\sqrt{2}\right)}^2+6_{c_4}{\left(\sqrt{3}\right)}^2{\left(\sqrt{2}\right)}^4+6_{c_6}{\left(\sqrt{2}\right)}^6)$

$=2(1\times 27+15\times 9\times 2+15\times 3\times 4+8)$

$=970$

$Since 0<{(\sqrt{3}-\sqrt{2})}^6<1, the smallest integer larger than {(\sqrt{3}+\sqrt{2})}^6 is 970$