\[\boxed{\text{1204\ (1204).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[n(n + 2)(n + 4)(n + 6) + 16 =\]
\[= \left( n^{2} + 6n \right)\left( n^{2} + 6n + 8 \right) + 16 =\]
\[= \left( n^{2} + 6n + 4 \right)^{2} - 4^{2} + 16 =\]
\[= \left( n^{2} + 6n + 4 \right)^{2}\ \]