All previous version of SQL Server Express were available in both web and full downloads. But I cannot find full download of SQL Server® 2016 Express. Does it exist?
Asked the same question on MSDN forums, not much luck: https://social.msdn.microsoft.com/Forums/en-US/sqlexpress/thread/4bfaa080-ec3b-4677-b2b8-cd0b60dc9486/.
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sql-server-express
sql-server-2016-express
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sql-server-2019-express
When you can't apply Juki's answer then after selecting the desired version of media you can use Fiddler to determine where the files are located.
SQL Server 2019 Express Edition (English):
SQL Server 2017 Express Edition (English):
SQL Server 2016 with SP2 Express Edition (English):
SQL Server 2016 with SP1 Express Edition (English):
And here is how to use Fiddler.
Once you start the web installer there's an option to download media, that being the full installation package. There's even download options for what kind of package to download.
Scott Hanselman put together a great summary page with all of the various SQL downloads here https://www.hanselman.com/blog/DownloadSQLServerExpress.aspx.
For offline installers, see this answer https://stackoverflow.com/a/42952186/407188
Source: Stackoverflow.com