First install and configure aws_cli
> pip3 install awscli --upgrade --user > aws configure
Now, enter your AWS Key, AWS Secret, your standard region (i.e. eu-west-1).
WIth your <S3-Bucket> name, you can now enter:
aws s3 ls s3://<S3-Bucket> --recursive | grep -v -E "(Bucket: |Prefix: |LastWriteTime|^$|--)" | awk 'BEGIN {total=0}{total+=$3} END {print total/1024/1024" MB"}'
With this method you can also inspect the size of other public S3-Buckets.
Have fun with AWS!
Yours
Frank