Why does Apple iCloud photosharing use googleapis.com?
Why your device communicates with google is simple - it’s where the bits are stored (among other places).

It’s widely reported that Apple will encrypt and store iCloud data in anonymous fashion on several cloud platforms with Google cloud (GCF) joining Microsoft Azure and Amazon (AWS) as vendors to Apple. 


https://www.engadget.com/2016/03/17/apple-icloud-google-cloud-platform/
https://www.computerworld.com/article/3045439/hybrid-cloud/apple-amazon-google-cloud-platform-itbwcw.html
http://www.zdnet.com/article/apples-hybrid-cloud-plan-google-aws-microsoft-azure-like-most-companies/
https://www.apple.com/business/docs/iOS_Security_Guide.pdf


The last Apple link/pdf explicitly acknowledges Apple uses AWS and Azure. I haven’t seen an updated doc publicly confirming that google cloud is part of the mix, it you are correct in seeing the traffic go there by design. 


  Each file is broken into chunks and encrypted by iCloud using AES-128 and a key derived from each chunk’s contents that utilizes SHA-256. The keys, and the file’s metadata, are stored by Apple in the user’s iCloud account. The encrypted chunks of the file are stored, without any user-identifying information, using third-party storage services, such as Amazon S3 and Windows Azure


So my reading is that Apple keeps the hashes and keys and identifiers in their own datacenters and on your device but then farms out bits of encrypted files all over the place so that they can keep the privacy and security promises made in the iOS security guide.