Expectation of $(X+Y+Z)^3$ Given that X,Y and Z are independent random variables and we are also given the moment generating functions of X,Y and Z, is there an easy way to find the expectation of $(X+Y+Z)^3$? 
Any help would be appreciated.

Given that $X,Y$ and $Z$ are independent random variables, so:
$E(X+Y+Z)^3=E(X^3+Y^3+Z^3+3(X+Y)(Y+Z)(X+Z))$
$= E(X^3+Y^3+Z^3+3X^2Y + 3X^2Z + 3XY^2 + 3Y^2Z + 3XZ^2 + 3YZ^2 + 6XYZ)$
$= E(X^3)+E(Y^3)+E(Z^3)+E(3X^2Y) + E(3X^2Z) + E(3XY^2) + E(3Y^2Z) + E(3XZ^2) + E(3YZ^2) + E(6XYZ)$
$= E(X^3)+E(Y^3)+E(Z^3)+3E(X^2)E(Y) + 3E(X^2)E(Z) + 3E(X)E(Y^2) + 3E(Y^2)E(Z) + 3E(X)E(Z^2) + 3E(Y)E(Z^2) + 6E(X)E(Y)E(Z)$
