How to keep environment variables when using sudo

First you need to export HTTP_PROXY. Second, you need to read man sudo, and look at the -E flag. This works:

$ export HTTP_PROXY=foof
$ sudo -E bash -c 'echo $HTTP_PROXY'

Here is the quote from the man page:

-E, --preserve-env
             Indicates to the security policy that the user wishes to preserve their
             existing environment variables.  The security policy may return an error
             if the user does not have permission to preserve the environment.

The trick is to add environment variables to sudoers file via sudo visudo command and add these lines:

Defaults env_keep += "ftp_proxy http_proxy https_proxy no_proxy"

taken from ArchLinux wiki.

For Ubuntu 14, you need to specify in separate lines as it returns the errors for multi-variable lines:

Defaults  env_keep += "http_proxy"
Defaults  env_keep += "https_proxy"
Defaults  env_keep += "HTTP_PROXY"
Defaults  env_keep += "HTTPS_PROXY"