Falling stone tiles have delayed the full opening of the building.
Council staff moved into the offices last year but retail units due to open in January remain empty because of ongoing repair work.
The council said it would be demanding compensation from main contractor VolkerFitzpatrick for lost rent.
County Councillor Mark Winnington, Cabinet member for Environment and Assets, told the BBC: “As soon as we know what it’s cost the tax payer, we will be going back to the builders.
“We want this reimbursing and if they don’t want to play ball we have a good legal department and we’ll take them to court on it.”
The BBC said VolkerFitzpatrick have been unavailable for comment.
The contractor was called back to the site in December 2011 after two stone tiles fell off and others came loose.
The council demanded that all 300 stone tiles used to clad the building should be removed and reattached.
Volker Fitzpatrick is paying for the extra maintenance work because the complex is protected by a 40-year guarantee, the authority said.