Permissions on at least part of the APT repos is broken:
Err:19 https://apt.dockerproject.org/repo/pool xenial/main amd64 Packages
403 Forbidden
W: The repository 'https://apt.dockerproject.org/repo/pool xenial Release' does not have a Release file.
N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: Failed to fetch https://apt.dockerproject.org/repo/pool/dists/xenial/main/binary-amd64/Packages 403 Forbidden
E: Some index files failed to download. They have been ignored, or old ones used instead.
Same problem with testing:
Err:18 https://apt.dockerproject.org/repo/pool xenial/testing amd64 Packages
403 Forbidden
W: The repository 'https://apt.dockerproject.org/repo/pool xenial Release' does not have a Release file.
N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: Failed to fetch https://apt.dockerproject.org/repo/pool/dists/xenial/testing/binary-amd64/Packages 403 Forbidden
E: Some index files failed to download. They have been ignored, or old ones used instead.