Factor completely. \[ v^{3}+k^{3} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $v^{3}+k^{3}=$ B. $v^{3}+k^{3}$ is prime.

Step 1 ：The given expression is a sum of cubes. The sum of cubes can be factored using the formula: \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\).

Step 2 ：Here, \(a = v\) and \(b = k\). So, we can use this formula to factor the given expression.

Step 3 ：The factored form of the expression \(v^{3}+k^{3}\) is \((v + k)(v^2 - vk + k^2)\).

Step 4 ：Final Answer: \(v^{3}+k^{3} = \boxed{(v + k)(v^2 - vk + k^2)}\)