My mother lives in Dublin Retirement Village, on the third floor. Her apartment features a small balcony, and this is where the squirrel has chosen to make its strange nest.
My brother, his wife, myself and other family members are frequent visitors to mom's place, and I happened to be there the first day the squirrel launched construction activities. By the end of the next day, he had largely completed construction. Squirrels begin with a sturdy latticework of small branches, which he harvested from nearby trees. Once these are in place to his satisfaction - there are hundreds of branches - he commences insulating the place with dead leaves. Many, many leaves are added, thoroughly chinking the gaps.
Sitting on the deck below the table is a small basket, and this may have been the perk that stimulated the squirrel to choose this site. His "bed" appears to be in the basket, which would provide yet another layer of easily insulated security. Ensconced within a well-built dray, the squirrel's body heat can keep the interior 20-30 degrees above the outside temperature. Sometimes two animals will share a dray, and that probably further increases the heat.
Gray Squirrels will sometimes make more than one dray, and this one may also have a more typical arboreal abode nearby. But, he seems to use the balcony nest as his primary residence.
Here is a brief video of the squirrel adding construction material. It's been educational to get a front row to the process; an activity that is normally difficult due to the lofty locations that they normally choose.