Is there any way to check total number of cases in specific backlog list?

The backlog count is the same as the overall count for the default  lists, however because the backlog page itself displays the total count, it won't be displayed in every report list.

Only for the custom created report lists the count differs and  we can check that by clicking on a particular case. We can view the case count on the top right corner of the support hub as shown in the screenshot.