Class:
global class DeleteoldCases{
    Public void SFDCDeleteoldCases(){
        List<Case> QueryCases = [SELECT Id FROM Case WHERE CreatedDate < LAST_N_MONTHS:18 ORDER BY CreatedDate ASC  LIMIT 9000];
        Integer QueryCount = database.countQuery('SELECT Count() FROM Case WHERE CreatedDate < LAST_N_MONTHS:18  LIMIT 9000');
            If (QueryCases.isEmpty())
            {
                return;
            }
            try{
                delete QueryCases;
            }catch(DmlException e) {
                System.debug('An unexpected error has occurred: ' + e.getMessage());  
            }catch(NullPointerException npe) {
                System.debug('The following exception has occurred: ' + npe.getMessage());         
            }finally{
            Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();         
            String[] toAddresses = new String[] {'CSAdmins@zynga.com'};        
            mail.setToAddresses(toAddresses);         
            mail.setSubject('Salesforce ZRM CaseDelete Status');         
            mail.setPlainTextBody('The Scheduled Apex job processed ' +QueryCount);         
            Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });
            }
    }
}

Test Class:

@isTest
public Class testDeleteoldCases {
    public static testMethod void testschedule() {  
        DeleteoldCases delca = new DeleteoldCases();
        delca.SFDCDeleteoldCases();
        
        Case newcase = new Case();
        newcase.Subject = 'Testing123456798';
        insert newcase;
List<Case> QueryCases = [SELECT Id FROM Case WHERE Subject = 'Testing123456798' ORDER BY CreatedDate ASC  LIMIT 9000];
        try {
            if(Test.isRunningTest()) {  
                QueryCases = null;
            }
            delete QueryCases;
        } catch(Exception e) {           
            system.debug('Failed to delete cases');
        }
    }
}