Will MSSQL 2014 standard version supports cloud sql or not ?
Not sure what you mean by "Cloud SQL". Microsoft Azure offers an Azure SQL DB service, however it is always running the latest version of their SQL Server database product, and it is missing some features like SQL Agent. You pay according to data size.
You can also use Azure SQL Managed Instance, that is similar to Azure SQL but has more SQL Server feature support, and it allows you to set a compatibility level, so if you need to exactly emulate SQL Server 2014, you can. You also get most of the Enterprise edition features as well, you can't limit them to Standard Edition.
Lastly, you can host a Windows virtual machine in Azure, or AWS, or other cloud providers, and install SQL Server 2014 there. You'lll need a separate license for non-Azure providers. If you go with Azure, Microsoft has options that includes the license fee as part of your monthly billing.
The Data Exposed playlist on Microsoft's Youtube channel has a few videos on choosing the right Azure DB service for your needs:
You will need to browse the list to find them, this forum post is embedding it as video.