The variance of a constant is zero.

Adding a constant value, c to a variable does not change variance (because the expectation increases by the same amount).
$ \hspace{30mm} \sigma_{x+c} = Var(X+c) = E[((X_{i} + c)-E(\overline{X} + c))^{2}] = Var(X) $

Multiplying a constant value, c to a variable increase the variance by square of the constant, c.
$ \sigma_{c*x} = Var(cX) = c^{2}Var(X)$

The variance of the sum of two or more random variables is equal to the sum of each of their variances only when the random variables are independent.
$ Var(X+Y) = Var(X) + 2 Cov(X,Y) + Var(Y)$
and $ Cov(X,Y) = 0 $