Pyle, 24, has made 28 appearances for the club since 2011, while Neville has appeared eight times for the first team since 2012.
"Both boys have shown great passion during their time here at the club, and I have seen Hugh grow immensely over the years since he was recruited in late 2010. The last six months he has really matured and that is showing in his rugby," Cockbain told the club's official website.
"Cadeyrn's development has been extraordinary, transforming from an AIS rower to a professional rugby player in a matter of years.
"The best thing about Cadeyrn is he is playing some great rugby in one of the toughest competitions in the world, and he will only get better."
Pyle is expected to face the British and Three Lions this summer.