if (x == begin()) {
        cout << "Удалить первый узел";
}
for (Node* i = begin(); i->next != end(); i=i->next) {
    Node* tmp = i->next;
    if (tmp && tmp == x) {
        i->next = i->next->next;
        delete tmp;
    }
}

avp@avp-ubu1:hashcode$ g++ huxilist.cpp
huxilist.cpp: In copy constructor ‘List::List(const List&)’:
huxilist.cpp:16:47: error: passing ‘const List’ as ‘this’ argument of ‘List::Node* List::begin()’ discards qualifiers [-fpermissive]
huxilist.cpp:16:60: error: passing ‘const List’ as ‘this’ argument of ‘List::Node* List::end()’ discards qualifiers [-fpermissive]
huxilist.cpp: In member function ‘List& List::operator=(const List&)’:
huxilist.cpp:37:27: error: passing ‘const List’ as ‘this’ argument of ‘List::Node* List::begin()’ discards qualifiers [-fpermissive]
huxilist.cpp:37:40: error: passing ‘const List’ as ‘this’ argument of ‘List::Node* List::end()’ discards qualifiers [-fpermissive]
huxilist.cpp: In function ‘int main()’:
huxilist.cpp:114:9: error: ‘List_m’ has not been declared
huxilist.cpp:114:23: error: ‘it1’ was not declared in this scope
huxilist.cpp:114:29: error: ‘listfile’ was not declared in this scope
avp@avp-ubu1:hashcode$

int delete_node (Node *x) {
    if (!x || !head)
      return -1;
    if (x == head) {
      head = x->next;
      delete x;
      return 0;
    }
    for (Node *t = head; t; t = t->next)
      if (t->next == x) {
        t->next = x->next;
        delete x;
        return 0;
      }
    return -1;
  }