Cuthbert and Robinson, who will move to Saturday's opponents Scarlets in the summer, will hit the half century as Blues hunt a fifth successive league victory to finish the campaign in style.
Coaching duo Dale McIntosh and Paul John make a number of changes to the side that claimed a hard-fought victory over Connacht Rugby last time out.
Centre Isaia Tuifua comes into the starting line-up for the derby clash while there is also a start for fly half Simon Humberstone with Gareth Davies missing the game through injury.
Robin Copeland will make his last appearance for the Blues at eight while Lewis Jones starts at scrum half as Lloyd Williams moves to the bench.
Coach Paul John said: "The confidence we have picked up in recent weeks has helped us. That showed against Connacht in the manner in which we fought back to get the win and we want to keep that going now until the final match.
"We wanted to finish the season positively after what happened at Ospreys and we have done that with four wins on a bounce. It will be difficult at Scarlets, they have qualified for the top European competition and they will want revenge after what happened at Judgement Day.
"It's always very tight when two regions go against each other, it's a local derby and it will be exciting for everyone.
"We make some changes as we have some aching bodies and injuries. However, those that go out on the field will want to finish strongly.
"A number of players will leave us after this game and it's important they finish on a high for Blues."
Cardiff Blues: 15 Dan Fish, 14 Alex Cuthbert, 13 Cory Allen, 12 Isaia Tuifua, 11 Harry Robinson, 10 Simon Humberstone, 9 Lewis Jones
1 Gethin Jenkins, 2 Matthew Rees (c), 3 Taufa'ao Filise, 4 Bradley Davies, 5 Filo Paulo, 6 Macauley Cook, 7 Josh Navidi, 8 Robin Copeland
16 Kristian Dacey, 17 Thomas Davies, 18 Scott Andrews, 19 Chris Dicomidis, 20 Ellis Jenkins, 21 Lloyd Williams, 22 Dafydd Hewitt, 23 Thomas Williams
27 - 15
HT: 10 - 8
10th May 2014
Parc y Scarlets