Assuming 5V output for moblie phone charger,
8000mAh is 40Wh (<100Wh), so you can bring 20 packs in cabin.

Assuming 20V output for large mac battery, 60,000mAh is 1200Wh (>160Wh), so under forbiden category.

In this discussion, you had better use Wh rather than mAh for clarity.