#### Answer

$2(x+2)(x^{2}-2x+4)$

#### Work Step by Step

$2x^{3}+16$
$=2(x^{3}+8)$
$=2(x^{3}+2^{3})$
To simplify the expression further, we will use the equation for the sum of two cubes: $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$.
Therefore,
$2(x^{3}+2^{3})=2(x+2)(x^{2}-2x+2^{2})=2(x+2)(x^{2}-2x+4)$.