I think you are looking for is Distributed Caching
Using the IDistributedCache interface you can use either Redis or Sql Server and it supplies basic Get/Set/Remove methods. Changes made on one node will be available to other nodes.
Using Redis is a great way of sharing Session type data between servers in a load balanced environment, Sql Server does not seem to be a great fit given that you seem to be caching to avoid db calls.
It might also be worth considering if you are actually complicating things by caching in the first place. When you have a single application you see the benefit, as keeping them in application memory saves a request over the network, but when you have a load balanced scenario, you have to compare retrieving those records from a distributed cached vs retrieving them from the database.
If the data is just an in memory copy of a relatively small database table, then there is probably not a lot to choose performance wise between the two. If the data is based on a complicated expensive query then the cache is the way to go.
If you are making hundreds of requests a minute for the data, then any network request may be too much, but you can consider what are the consequences of the data being a little stale? For example, if you update a record, and the new record is not available immediately on every server, does your application break? Or does the change just occur in a more phased way? In that case you could keep your in process memory cache, just use a shorter Time To Live.
If you really need every change to propagate to every node straight away then you could consider using a library like Cache Manager in conjunction with Redis which can combine an in memory cache and synchronisation with a remote cache.
DistributedCachingsolution provided byRedisand other system