Database mail in Azure VM with SQL Server installed on it
Check out this link - basically, you need to use an authenticated relay (like sendgrid) when sending from an Azure VM. 

There are some exceptions:


Enterprise Agreement subscriptions don't have this restriction
Pay-As-You-Go subscriptions can submit an exemption request and if approved you will not have to use an authenticated relay. Note, this only applies to VMs. PaaS services cannot be exempted.


All other subscriptions do not have the exemption option - you must use an authenticated relay.