I have a MCP4725 Breakout Board - 12-Bit DAC w/I2C Interface.
I have tested the library Adafruit_MCP4725 with the examples sinewave and trianglewave using my arduino UNO.
My question is:
Can I use the eeprom of the MCP4725 Breakout Board to store a wave and use only MCP4725 Breakout Board without arduino UNO?
Did you even check how much EEPROM the chip's got on board? Check the datasheet.
The MCP4725 device has a 14-bit wide EEPROM
memory to store configuration bit (2 bits) and DAC
input data (12 bits)
The only reason for that EEPROM is so that the chip can maintain it's settings through a power loss. It only stores one output value, not a waveform's worth.
The answer is no.