Cascading a filter with itself to form a higher-order filter?
Replace your $\alpha$ with the following to see if it helps:

fs = 16000;
fc = 3500;
wc = 2*pi*fc/fs;

L = 5;            % order of the cascade
B = 2^((L-1)/L);
C = cos(wc);
M = B-C-1;
N = 1+C-B*C;
alfa = ( -N + sqrt( N*N - M*M ) )/M;


I've got the following plots, compared to your posted $\alpha$ calculation.