I would like to ask a question on the sum of variance. I understand that for 2 random variables X and Y, sum of variance equals variance of sum Var(X) + Var(Y) = Var(X+Y) only if X and Y are independent.

My question is, what if we are dealing with 3 random variables X,Y and Z. What property does the 3 random variable need to have for the sum of variance to be equal to the variance of sum Var(X) + Var(Y) + Var(Z) = Var(X+Y+Z). Is pairwise independence of the variables sufficient OR do all 3 variables have to be mutually independent for the above statement to hold?

Please explain. Thank you!