ATmega 32A and 2560 R3 register to pin mapping?
What is ATmega2560 R3? There is ATmega2560 MCU or Arduino Mega R3. do you want the mapping of pins of Arduino Mega or the pins of the ATmega2560 MCU.

The mapping of pins of the ATmega 2560 chip is in the datasheet.

The mapping of the Arduino Mega pins to ATmega2560 pins and registers is in the schema of the board or in the Arduino AVR boards package variants mega folder.

The link "Arduino's 2560 pin mapping" in your question shows the mapping too. Registers are PA, PB,... and every register covers to 8 pins with the 8 bits of the register. For example PB3 is pin 50 of the board.