Not sure why you created those squares in the middle of your gate?
Since you didn't put diagonal bracing in your gates, you should really run a cable from the top hinge corner to the opposite bottom cable so they wont sag on you. I would also install inside metal brackets to your corners so they don't come apart.
The squares are just a byproduct of the diagonal bracing on the gate. I couldn't just run screws and box the 4x4's without some support or it would sag and wouldn't be square. I do have steel cable that I'll be running diagonal from the top of the posts to bottom of the next post, but I'm not sure how much I'll actually need it. The posts are already tied to the other posts by the 2x4's, so they really shouldn't be able to sag.