if you are in the USA, wall outlet voltage can be anywhere from 115 to 127 volts depending on location...
the best way to power an LED with such a small battery is to use a charge pump. back in the day i used to use LM3909 ICs for this, but that chip has been discontinued, but chips like this
https://www.onsemi.com/products/power-management/led-drivers/dc-dc-led-drivers/ncp5603 are in current production... just do a search for "low voltage LED charge pump" to find others.... running the LED through a resistor will waste some energy as heat, and when the battery gets down to the LED's forward voltage the LED won't light... a charge pump will keep the LED lit for a lot lower battery voltages. white and blue LEDs have a forward voltage of about 3.6V so your 3V battery, if it lights them at all will not light them to full brightness. the charge pump will keep the same LEDs lit at near full brightness all the way down to about 1.25V battery voltage.