Factor. \[ 27+8 x^{3} \]

To factor \( 27 + 8x^3 \), we can recognize it as a sum of cubes. Specifically, \( 27 = 3^3 \) and \( 8x^3 = (2x)^3 \). The sum of cubes formula is \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). Here, let \( a = 3 \) and \( b = 2x \). Applying the formula: \[ 27 + 8x^3 = (3 + 2x)((3)^2 - (3)(2x) + (2x)^2) = (3 + 2x)(9 - 6x + 4x^2). \] Thus, the factored form is: \[ \boxed{(3 + 2x)(9 - 6x + 4x^2)}. \]