seems to me you need to buy some concrete anchors which are threaded. My parents porch railing is secured to the brick porch in this fashion.

You have a number of options, all which involve and drill and masonry bit. As the other poster mentioned, there are screws designed specially to drive into brick and concrete. The most common brand name is "Tapcon" and you can find them in just about any good home center or hardware store. You drill a pilot home and then drive the screw. The manufacturer sells drills bits just for this purpose but if you already have the correct size bit, you can use that. I've used them on any number of occasions and they work quite well.

Another option is just a plastic anchor. Basically you drill the appropriate sized hole and put the anchor in the hole. Then drive your screw into the anchor. In that case, I'd suggest using a stainless steel screw to prevent rust.

Good luck!

Here is a link that might be useful: Tapcon Website

Thanks to both of you for the advice. I'll most likely use the Tapcon product. My biggest concern is the weight of the box, so will just read a little more about this process and then give it a try. Thanks again for the advice!

If you use tapcons, get the ones with a hex head style cap, A nut driver on a cordless impact tool is the best way to install these. Make sure you use the right size masonry bit provided by tapcon, drill the hole 1/4" deeper than the fastener, clean out the dust.