Boxer says, “I will work harder” in several places in the book Animal Farm.
Unfortunately, there are a few different editions of the book. I cannot give you specific page numbers, because your edition might be different than mine. What I will do is show you where the quotes are, so that you can find the page numbers easily.
At the beginning of chapter 3, Boxer is described as a strong laborer who always volunteers for more work around the farm.
His answer to every problem, every setback, was "I will work harder!"—which he had adopted as his personal motto. (bottom of the third paragraph at the beginning of chapter 3)
In chapter 6, Boxer finds his first motto insufficient and adds a second, so this is another page where you will find the phrase.
His two slogans, "I will work harder" and "Napoleon is always right," seemed to him a sufficient answer to all problems. (4th paragraph of chapter 6, 3rd to the last sentence)
This demonstrates that Boxer has total faith in Napoleon, and wants to help him carry out his plans.
“I will work harder” is also found at the bottom of the second paragraph of chapter 7 and at the bottom of the ninth paragraph of chapter 9, where Boxer tries to say the words even as he is weakened and dying, showing his unfailing faith until the end.
In the second to last paragraph of chapter 9, Napoleon even reminds everyone of Boxer’s maxims in a speech.
Napoleon ended his speech with a reminder of Boxer's two favourite maxims, "I will work harder" and "Comrade Napoleon is always right"--maxims, he said, which every animal would do well to adopt as his own.
Of course Napoleon would prefer that Boxer’s work effort and loyalty were taken up by all of the animals.
At the end of chapter 4 you will find your second quote in an exchange between Boxer and Snowball.
He is dead," said Boxer sorrowfully. "I had no intention of doing that.
I forgot that I was wearing iron shoes. Who will believe that I did not do this on purpose?"
"No sentimentality, comrade!" cried Snowball from whose wounds the blood was still dripping. "War is war. The only good human being is a dead one."
"I have no wish to take life, not even human life," repeated Boxer, and his eyes were full of tears.(about 6 paragraphs from the end of chapter 4)
This shows that Boxer is kind and caring, and holds even enemy life as valuable. It is another example of his status as the common man, whom he represents.