There is a servo/sensor shield for the Arduino Mega that can control up to 54 servos. This shield will only fit the Mega, unlike the usual 14 servo Arduino shield, which is shaped to fit most Arduino boards.
Here is an easier to view diagram:
It is possible, and advisable, to supply power via the screw terminals from an external power source, rather than use the Arduino's own power. Even just one servo can have difficulty in working from the Arduino's on board power supply, especially if just using USB to power the Arduino. However, even with the use of an external power source powering the shield, I have my doubts as to whether the shield could support 21A without burning out. Someone may be able to clarify this.
You may find this page, Servo Shield, useful:
MEGA Sensor Shield
The Arduino MEGA has many more I/O pins (54 Digital pins and 16 Analog
pins)than a standard Arduino. This shield also has connectors
specifically for some external devices like an SD Card, Radio
communications (Bluetooth and others). It also has an option to power
the "V" pins on all the Digital I/O 3-pin groups from an external
power supply instead of the Arduino +5V. This is good for large
numbers of servos etc. The "Analog" 3-pin groups still use the Arduino
+5V which is better from an electrical noise perspective.
This version has two options of +5V supply to all the "V" pins:
- Jumper on: +5 comes
from the Arduino. Should be limited to about 300 ma
- Jumper off: +5 (or
other appropriate voltage) comes from an external supply connected to
the blue terminal strip. External power Ground must also be connected
to the blue terminal strip.
Using an external supply allows more current than the Arduino or Mega
can supply, such as current for control of many servos or relays, and
other attached devices. Usually this is +5V because most external
devices require it. It is possible to use +6 volts if ALL the attached
devices are the same such as Servos with that rating.