In this method, the first node of the circular doubly linked list is deleted. For example - if the given list is 10->20->30->40 and the first node is deleted, the list becomes 20->30->40.

Deleting the first node of the circular doubly linked list is very easy. If the list contains one node, delete the node. If the list contains more than one node, then create two nodes - temp and firstNode both pointing to the head. Using temp node, traverse to the last node of the list. Make next of head as the head node and update all links. Finally, delete the first node. The function pop_front is created for this purpose. It is a 4-step process.

```void pop_front() {
if(head != NULL) {

//1. the list contains one node, delete
//   make the head null
if(head->next == head) {
head = NULL;
} else {

//2. if the list contains more than one node,
//   create two nodes - temp and firstNode, both
//   pointing to head node
Node* temp = head;
Node* firstNode = head;

//3. using temp node, traverse to the last node
while(temp->next != head) {
temp = temp->next;
}

//4. Make head as next of head, and
//   update links
head = head->next;
head->prev = temp;
temp->next = head;
free(firstNode);
}
}
}
```

The below is a complete program that uses above discussed concept of deleting the first node of the circular doubly linked list.

```#include <iostream>
using namespace std;

//node structure
struct Node {
int data;
Node* next;
Node* prev;
};

class LinkedList {
private:
Node* head;
public:
LinkedList(){
head = NULL;
}

//Add new element at the end of the list
void push_back(int newElement) {
Node* newNode = new Node();
newNode->data = newElement;
newNode->next = NULL;
newNode->prev = NULL;
if(head == NULL) {
head = newNode;
newNode->next = head;
newNode->prev = head;
} else {
Node* temp = head;
while(temp->next != head)
temp = temp->next;
temp->next = newNode;
newNode->next = head;
newNode->prev = temp;
head->prev = newNode;
}
}

//Delete first node of the list
void pop_front() {
if(head != NULL) {
if(head->next == head) {
head = NULL;
} else {
Node* temp = head;
Node* firstNode = head;
while(temp->next != head) {
temp = temp->next;
}
head = head->next;
head->prev = temp;
temp->next = head;
free(firstNode);
}
}
}

//display the content of the list
void PrintList() {
Node* temp = head;
if(temp != NULL) {
cout<<"\nThe list contains: ";
while(true) {
cout<<temp->data<<" ";
temp = temp->next;
if(temp == head)
break;
}
} else {
cout<<"\nThe list is empty.";
}
}
};

// test the code
int main() {
LinkedList MyList;

//Add three elements at the end of the list.
MyList.push_back(10);
MyList.push_back(20);
MyList.push_back(30);
MyList.push_back(40);
MyList.PrintList();

//Delete the first node
MyList.pop_front();
MyList.PrintList();

return 0;
}
```

The above code will give the following output:

```The list contains: 10 20 30 40
The list contains: 20 30 40
```