Recently Microsoft added a feature that I requested in early 2016. Back then I would hear from customers about failed deployments to find out that it was the limitation on the core count. All they needed to do was to open a ticket to request a core quota increase. The problem comes when someone else had increased the quota already so you had no idea what the actual limit was at that point in time.
Eventually Microsoft exposed the current quota for cores in the portal when submitting a ticket for a quota increase. That was better but we still needed to see more info. Recently Microsoft added the capability to see Azure Usage and Quotas. You can see this by opening the Subscriptions blade, select a subscription and click on Usage + Quotas. You can also get to the same place through the Billing feature which is still in Preview at the time of this writing.
Here you can see a few quotas listed with the usage. Only a small subset are listed today but expect to see more added soon. There is also an integrated support experience from within this blade to allow you to request an increase.
Note: Core quotas are per region accessible by your subscription. So you would need to request an increase based on the region you are deploying into as well as the size of VM series.
Free Trial subscriptions are not eligible for limit or quota increases. You will need to upgrade to a PAYG subscription.
For a complete listing of all the subscription and service limitations, quotas and constraints, go to this link.