Show your work and the associated numbers with each player.
Once you do that you will see that your math is off.
CapFriendly.com Armchair-GM User-Generated Roster
FORWARDS (14)
Right wing: James Neal ($5,750,000) - Zack Kassian ($1,950,000) - Josh Archibald ($1,000,000) - Alex Chiasson ($2,150,000) - Tomas Jurco ($750,000)
Centre: Connor McDavid ($12,500,000) - Leon Draisaitl ($8,500,000) - Colby Cave ($675,000) - Gaëtan Haas ($925,000) - Riley Sheahan ($900,000)
Left wing: Joakim Nygård ($925,000) - Ryan Nugent-Hopkins ($6,000,000) - Jujhar Khaira ($1,200,000) - Markus Granlund ($1,300,000)
DEFENSE (7)
Right: Kris Russell ($4,000,000) - Ethan Bear ($720,000) - Matthew Benning ($1,900,000) - Adam Larsson ($4,166,666)
Left: Darnell Nurse ($3,200,000) - Oscar Klefbom ($4,167,000) - Andrej Sekera ($3,000,000)
5.5 cap hit with the buyout below
GOALTENDER (2)
Mikko Koskinen ($4,500,000) - Mike Smith ($2,000,000)
AHL BURIED (2)
Sam Gagner ($2,075,000) - Brandon Manning ($1,175,000)
BUYOUTS (3)
Andrej Sekera ($2,500,000) - Benoit Pouliot ($1,333,333) - Eric Gryba ($300,000)
RETAINED SALARY TRANSACTIONS (1)
Milan Lucic ($750,000)
DETAILS
Roster Size: 23
Salary Cap: $81,500,000
Cap Hit: $81,461,999
Cap Space: $38,001
This is without putting Brodziak on LTIR which would have freed up ~$1M. And now with Larsson on LTIR we've got even more space.