Progress
After allowing the square sit for a day the liquid cement did not adhere to the joints correctly and as a result when I lifted up the corners one side twisted and broke off. I had to take off the broken corner and re-glue the square before I could move on with assembly. I was running into issues with the sturdiness of the cube. As a result my Dad gave me the idea of filling the pvc pipes with concrete on order to add weight to it. I created a mixture that was fairly fluid and used a funnel to help fill out the pipes. Then I would lift up the corners to allow gravity to move the concrete further down the pipe. I checked up on the base throughout the week and added another layer after the first one dried to ensure the base was heavy enough.
For the celling I added another pipe for support and used zipties to hold up the wire racks.