Cubert is the 12-year-old clone of Professor Farnsworth, though the two of them have a father/son relationship. Cubert was created from DNA that the professor scraped off of a growth on his back.
His nose is pig-like because the professor left him in the test tube too long and his nose got smushed up against the glass.
Cubert was first introduced to the crew at Planet Express in the episode "A Clone Of My Own." He was arrogant and condescending, picking on every character, and poking holes in all of the professor's scientific explanations, and refused to take over his work (which is what he was cloned for). By the end of the episode, he accepted his purpose and admitted he DID want to be just like his dad.
He is best friends with Hermes' son Dwight, and attends boarding school with him. In the episode "The Route Of All Evil," the two boys get suspended for fighting with a bully, and since they keep getting underfoot at the office, Hermes tells them to get a job, so they start their own delivery company, Awesome Express. At first, they just have a paper route, but they soon expand and take over Planet Express. All in an effort to make their fathers proud.
In the episode "Bender Should Not Be Allowed On Television," Cubert and Dwight get in trouble for emulating Bender after the robot joins the cast of All My Circuits. It is also in this episode that we learn that Cubert doesn't have a birthday, because he technically didn't have a birth. So he can celebrate the day the professor scraped his DNA from the growth on his back with a fork.
Cubert: "Your explanations are pure, weapons-grade balonium! It's all impossible!"
Professor Farnsworth: "Nothing is impossible! Not if you can imagine it! That's what being a scientist is all about!"
Cubert: "No, that's what being a magical elf is all about."
Cubert: "Hey, Dad. What sort of useless contraption are you half-baking today?"
Professor Farnsworth: "Eh wha--? Oh, this is my latest invention; a device that lets anyone sound exactly like me."
Cubert: *speaking into the machine* "Good news, everyone! I'm a horse's butt!"
Professor Farnsworth: "I am? That's not good news at all, you little--"
Cubert: *speaking into the machine* "WHAAAA!"
Cubert: *speaking into the voice machine, sounding like the professor* "This is Professor Farnsworth. I have an important delivery for you and your dumb crew. You must deliver a package to Dog Doo 8, a planet at the edge of the universe. Sorry I can't come down to say goodbye, but I'm busy inventing useless junk."
Dwight: *using the voice machine to sound like the professor* "And I smell bad!"
Dwight: "Our dads are never impressed, no matter what we do."
Cubert: "Maybe we should start a fire."
Cubert: "Hey, Leela-- help me apply these flame decals I got in my cereal; they'll make the ship go faster."
Leela: "And what's your scientific basis for thinking that?"
Cubert: "I'm twelve."
Cubert: "This show is awesome! When I grow up, I'm going to have SO MUCH amnesia!"
Dwight: "Me too! I mean, I have it now, but I forgot."
Cubert: "Well, mine's louder!"
Bender: "Cram a ham in it, you twerps!"
Leela: "Do you two have to imitate everything you see on TV?"
Cubert: "Um, we're twelve, so YES."
Dwight: "Hold up, Cubert-- you're a clone of the professor; do clones even have birthdays?"
Cubert: "Um, duh."
Dwight: "...duh what?"