Rewrite the expression by factoring out $(u+8)$. \[ 6 u^{2}(u+8)+(u+8) \]

Step 1 ：Rewrite the expression by factoring out \((u+8)\).

Step 2 ：The expression given is a sum of two terms, both of which contain the factor \((u+8)\). To simplify the expression, we can factor out \((u+8)\) from both terms. This is similar to the distributive property of multiplication over addition, but in reverse. Instead of distributing a factor to each term in a sum, we are 'undistributing' a common factor from each term in the sum.

Step 3 ：The expression $6 u^{2}(u+8)+(u+8)$ can be factored to $(u+8)(6u^2+1)$. So, the factored form of the given expression is \(\boxed{(u+8)(6u^2+1)}\).