Do you want to store data in the cloud, but do not want to install Linux servers, load balancers and do server maintenance on a daily basis the rest of your life?
One solution is to use Amazons AWS services.
For storing data you can use the NoSQL database DynamoDB. See a guide here. However accessing data directly from an app is not a good option. You will need to store your keys and database credentials directly in the app. Hackers can easily decompile the app and reveal the credentials.
You need a middle layer to handle secure access to the database without exposing credentials to the DynamoDB. You can write your own in a various languages, but that again requires a real server somewhere or what can you do?
The solution is to use Amazon Cognito. It handles the middle layer logic without writing any backend code or managing any infrastructure. Take a look here for Amazon Cognito.