I tried the same with Bing Chat
"A single feather and a bucket full of feathers have the same density because density is a property of the material itself, not the amount of material. Density is defined as mass per unit volume, so the density of a feather remains the same whether it is alone or in a bucket with other feathers. Is there anything else you would like to know?"
My approach:
First, find the density of a feather, to find that, I need to find what they are made of. A search suggests they are made of keratin, and that has a density of about 1.32g/cm³
A bucket of feathers consists of a bucket, some feathers, and lots of air.
What is the density of a bucket? Most buckets are made of polypropylene. I found multiple sources that give slightly different values for the density, probably because they are different plastic suppliers and produce a slightly different product, but they are around 0.9g/cm³. Most importantly, they are all below 1.32g/cm³.
Air is less dense than both of those. Do I need to look up values or cite sources?
Therefore, if the bucket is made of polypropylene, a bucket of feathers has a lower density than a feather.
If the bucket is made of something else, like for example stainless steel or aluminium, then it could have a higher overall density, depending on how big the bucket is, how thick the walls of it are, etc; how tightly you pack the feathers.