1) draw your parts as per your post.
2) then "merge" the cube with the 2 in cyl.(don't do anything with the 1 in cyl, yet) Note you should get a message that informs you you have a watertight model.
3) then use the "difference" function to remove the 1 in cyl.(pick the cube/cyl comb then the 1 in cyl.
4) then use the "disconect" surfaces funtion and pick the model.
5)then use select all and use the "union" funtion to remove the inner parts.
By the way I always do a "save" between every operation just in case it dosn't like it.
Let me know if this is not what you want.