Massey, 22, has signed until 2017, while 22-year-old Eastman has agreed a deal until 2016 and Kent, 18, will stay with the League One side until 2018.
All three have featured prominently this term, with teenager Kent making his first senior start in August.
"It's been a long journey to get to where I am and I can't thank everyone enough," he told BBC Essex.
"I'm feeling comfortable in the team and I'm getting used to my surroundings.
"Once I started playing a few games I think the club wanted to reward me. I couldn't turn it down - I love playing here."
Young U's midfielder Sammie Smzodics also signed a contract until 2018 last week.

And now an eight-year-old Swansea schoolboy is to quiz him about how it felt via Twitter.
Rhys Maguire-Stokes was among 25 pupils from Blaenymaes primary at a live link-up with the International Space Station on Tuesday.
It was one of 10 UK schools - and the only one from Wales - at the event in Liverpool.
While there was not time for Rhys to ask his question live, it has been tweeted to the astronaut to answer.
Class teacher Amy Smith said Rhys was chosen to be the school representative to ask Maj Tim as he floated 264 miles above Earth: "How did it feel to walk in space?"
"It's a shame there wasn't time for him to ask his question live but we've tweeted Major Peake and will wait for his answer," she said.
"The kids have had a fabulous day and as soon as they saw Major Peake on the screen, their faces just lit up."
Mrs Smith entered the school into a competition run by the Times Education Supplement's website to be one of those gathering at the World Museum, as part of the "Cosmic Classroom" event.
The feed was then relayed to other schools around the country; in all 10,000 children were taking part.
As well as answering pupils' questions, Maj Peake also demonstrated a number of scientific activities in space, which the children could copy in their classrooms.
"He was absolutely brilliant and did lots of tricks for them, showing how he floated and doing tricks with water to make it go into bubbles," said Mrs Smith, who took pupils from years 4 and 5.
"The children were very excited and have been since the moment they were told they were going.
"I think it's fantastic for him to take time out of his mission in space to talk to the children and he has really inspired them. A few of them are now saying they want to go into space too and be able to float."
The children have been studying space as a topic since Christmas and will be holding a class assembly and creating a class book to mark their time with Maj Tim.
The European Space Agency astronaut launched to the orbiting platform on 15 December and is due to stay aboard until June. The International Space Station is currently above the south Atlantic
He described his first walk in space as "exhilarating".
Colchester United have handed new deals to striker Gavin Massey and defenders Tom Eastman and Frankie Kent.
[NEXT_CONCEPT]
Major Tim Peake made history when he became the first British person to walk in space.