I have the following code that sends a mass email out based on a end date being past due. Being a very new apex developer I need some help with the following task. The main list of people receiving the mass email is setup in the getSPEEmailAddresses module. The problem I am having is that there is a public group defined in the getpublicgroupaddresse module that I need to cc on each email going out in the getSPEEmailaddresses module and I don't know how to go about doing that. Can anyone adjust the below code to accomplish that task?

/**************************************************************************/
//The SPEs past due Notice Emailer
//
//This class can be scheduled to run nightly to send emails to SPE
//owners, and the public group called SPE_Pastdue_Notification
// when the End DAte (End_Date__c) is within 14 days of being past due
// and the routing status = approved.
//
/***************************************************************************/

global class SPEs_Pastdue implements Schedulable{


     //mandataory function called by the Apex Scheduler
  //**************************************************
  global void execute(SchedulableContext SC) {
        //**************************************************
        sendmail(); // our main function that does the email sending
     }//end execute

  //Get email addresses of people pastdue SPEs by 14 days
//**************************************************
    public List<Id> getSPEEmailAddresses(Date CalDate) {     
    //**************************************************
         List<Id> mailToIds = new List<Id>();
         
         //find a list of SPEs with overdue end dates
         Sales_Policy_Exceptions__c[] c = [SELECT Id, End_Date__C, Routing_Status__c, owner_email__c
             FROM Sales_Policy_Exceptions__c
             WHERE End_Date__c <= : CalDate
                            AND Routing_Status__c = 'Approved'
             ];                
                         // Old Date samples 
          // DAY_IN_MONTH(CloseDate) = : Day
      // AND CALENDAR_MONTH(CloseDate) = : Month
                        //  AND CALENDAR_Year(CloseDate) = : Year
           
           
   //add the list of Sales_Policy_Exceptions__c to a list       
         for(Sales_Policy_Exceptions__c recipient : c) {
         
          
           System.Debug('\n*******Found Sales_Policy_Exceptions__c Recipient');
                     
           if (recipient.owner_Email__c != '')
           {
            mailToIds.add(recipient.Id); // add to email SPE array
            System.Debug('\n*******Recipient: '+ recipient.owner_email__c); 
           } else {
            //Just add to chatter array
            System.Debug('\n*******NO Recipient');
           } //end if        
         } //end for loop

         return mailToIds;   //return the list
      } //end getSPEEmailAddresses()
   
    //**************************************************
    public List<String> getPublicGroupAddresses() {
    //**************************************************
  List<String> idList = new List<String>();
  List<String> mailCCAddresses = new List<String>();
        List<ID> mailCCAddressesID = new List<ID>();
  Group g = [SELECT (select userOrGroupId from groupMembers) FROM group WHERE name = 'SPE_Pastdue_Notification'];
   for (GroupMember gm : g.groupMembers) {
   idList.add(gm.userOrGroupId);
  } //End group
  User[] usr = [SELECT email FROM user WHERE id IN :idList];
  for(User u : usr) {
   mailCCAddresses.add(u.email);
            mailCCAddressesID.add(u.id);
  } //end for loop
return mailCCAddresses;      
}   //End getPublicGroupAddresses

//**************************************************
    public void sendMail() {
    //**************************************************
   //define variables     
   String debugAddress = 'xxx@newpagecorp.com';
   String SPEEmailTemplateName = 'Opportunity_Past_Due_Notice';  
   String debugMessage;
         String[] toAddresses;

            Date CalDate = date.Today().addDays(14);

            System.Debug('Date '+CalDate);


   // build the Overdue list

   //get the list of people with overdue Sales_Policy_Exceptions__c - this can justifiably come back empty.
         List<Id> SPEIdsList = getSPEEmailAddresses(CalDate);
            List<Id> SPEgroupList = getPublicGroupAddresses();

   //Set the templates
         EmailTemplate SPETemplate = [select Id,Name,Subject,body from EmailTemplate where DeveloperName = :SPEEmailTemplateName];
 
         if(SPETemplate != null && SPEIdsList.isEmpty() == false)
         {

             Messaging.MassEmailMessage SPEMail = new Messaging.MassEmailMessage();
       
             SPEMail.setTargetObjectIds(SPEIdsList);
             SPEMail.setTemplateId(SPETemplate.Id);
             SPEMail.setUseSignature(false);
             SPEMail.setSaveAsActivity(true);

             // Send the email
             try {
              Messaging.sendEmail(new Messaging.MassEmailMessage[] { SPEMail });
                    System.Debug('Mail sent');
             }catch(Exception e)
             {
              System.Debug(e);
             }
          
         }
         else
         {
             System.Debug('SPECronJob:sendMail(): Either an email template could not be found, or no opportunities are overdue');
         }//end if

               
  }//end sendMail()
}   //SPEs_Pastdue end