I have also put the charges along the axis as you have described. So the vector caused by each charge:
(1,0,0) \ \ a_1 = -l\hat{i}
(0,1,0) \ \ a_2 = -l\hat{j}
(0,0,1) \ \ a_3 = -l\hat{k}
(1,1,0) \ \ a_4 = -l\hat{i}-l\hat{j}
(0,1,1) \ \ a_5 = -l\hat{j}-l\hat{k}
(1,0,1) \ \ a_6 =...