Minha solução

// Copyright (c) 2019, the Dart project authors.  Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

import 'package:default_app/bloc/counter_cubit.dart';
import 'package:flutter/material.dart';
import 'package:flutter_bloc/flutter_bloc.dart';

void main() => runApp(const MyApp());

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      debugShowCheckedModeBanner: false,
      theme: ThemeData(
        useMaterial3: true,
        primarySwatch: Colors.blue,
      ),
      home: BlocProvider(
        create: (context) => CounterCubit(),
        child: const MyHomePage(title: 'Contador com Cubit'),
      ),
    );
  }
}

class MyHomePage extends StatefulWidget {
  final String title;

  const MyHomePage({
    Key? key,
    required this.title,
  }) : super(key: key);

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  CounterCubit get cubit => context.read<CounterCubit>();

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
        centerTitle: true,
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: [
            const Text(
              'You have pushed the button this many times:',
            ),
            BlocBuilder<CounterCubit, int>(
              builder: (context, value) {
                return Text(
                  '$value',
                  style: Theme.of(context).textTheme.headlineMedium,
                );
              },
            ),
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        onPressed: cubit.increment,
        tooltip: 'Increment',
        child: const Icon(Icons.add),
      ),
    );
  }
}

Classe counter_cubit

import 'package:bloc/bloc.dart';

class CounterCubit extends Cubit<int> {
  CounterCubit() : super(0);

  void increment() => emit(state + 1);
}