Maybe this is what you want:
B0 = whatever
V = whatever
sigma_sum = V;
M = eye(4); % <-- I am guessing that you really need eye(4) here instead of ones(4)
for t=1:(T-1)
M = M + B0^t; % <-- Used ^t instead of .^t here ... again I am guessing a bit here
sigma_sum = sigma_sum + M*V*M';
end