"Once I got in there, I wanted to do what I could to help my team win," said Cubbage, who finished with 14 points, 11 rebounds, and two blocks.
Senior guard Ron Curry scored 13 points with six assists and four steals and sophomore forwards Jay Howard and Matt Risse each scored 13 for Paul VI (8-0), the No. 1 team in The Inquirer's South Jersey rankings.
Junior forward Tristan Polnitz scored 10 and freshman guard Alec Warren added nine for Shawnee (8-3), which lost its third in a row.
"There were some good things that can come out of this game," Shawnee coach Joe Kessler said. "I thought our kids really hung in there and battled."
Kessler said Paul VI is "the best team around," because of the Eagles' balance and athletic ability.
"They're good at every position," Kessler said.
Paul VI coach Tony Devlin was pleased with his team's play in the second quarter, when Cubbage and senior guard Kris O'Connor stayed glued to the bench because of foul trouble.
Paul VI received strong work in that quarter from Howard and Risse, as well as reserves Pat Kennedy and Tim Terifay.
"The big-picture thing for us tonight was the bench," Devlin said. "We've talked about that. If we're going to go anywhere in March, we're going to need the support from our bench."
Still, Shawnee was within 28-26 at halftime after a strong second quarter that included six points by Polnitz and a pair of three-point jumpers by Warren.
Cubbage took over in the third quarter, collecting seven rebounds and four points as well as a block and an assist. The latter was a fastbreak feed to Curry for a dunk that gave the Eagles a 44-30 lead and ignited a celebration in the Paul VI student section behind the basket.
"He's just so strong," Kessler said of Cubbage. "Not only is he athletic, he's so strong in there. He gets position, and you can't move him out of there."