I am sharing below how this error was fixed for me.
Go to Sql Server Configuration Manager.

Go to the Properties of the instances of SQL Server Analysis Services that you want to run.

Provide the proper Account Name that you have correct credentials for. In my case:

Click the "Browse" button from the image above to reach this window:

Click "Advanced..." from the image above to reach this window:

Click "Find Now" from the image above and find the user you have proper credentials for to login with:

Click "OK" from the image above. Then "OK" again from the following window:

Provide correct password for the user that you chose:

Click "OK" from the image above. Click "Yes" to restart the service:

Confirm that the service is running and process again your cube:

This time the data cube was processed successfully:
