The Y Gaer (Welsh for 'fortress') cultural hub is the redevelopment of the Grade II Listed Shire Hall, including a new modern library.
It opened yesterday with a low-key ceremony.
This is due to the general election and purdah rules so that no political gain can be made from the occasion.
Powys County Council said it will have an official opening ceremony next year, but has not released details so far.
The project has been delayed for months and was supposed to have opened last year and then on March 1 this year.
Costs have also ballooned to £14.2 million, over £5 million more than expected.
Councillor Karen Laurie-Parry who represents Bronllys as an independent asked if there had been penalty clauses in the contract for the delays.
She said: “To undertake a forensic analysis could possibly result in clawing back much needed finance for the authority and at least create confidence in Powys management."
The questions were directed to Councillor Rachel Powell who represents Beguildy as an independent and is the portfolio holder for culture which includes libraries.
Councillor Powell said: “There have been delays experienced on the Y Gaer construction programme due to the supply of Alsecco stone cladding material and the subsequent fabrication and installation of the cladding to the building exterior.
“This delay was caused by a third party supplier to Kier and was influenced by the availability of material due to quarrying restrictions, the complexity of design and the supplier’s own programming, and as such could not have been foreseen by the project management board.
“There has been no cost incurred by the council due to the delay since it has occurred during the fixed contract sum period.
“Once the construction work on Y Gaer is complete, attention will turn to reviewing the project; this will include colleagues from Legal and Procurement in order to work through the contract.
“The review will put forward appropriate recommendations/learning for future action.”
Public meetings and protests have taken place in Brecon with people and councillors concerned about the project.
In July it emerged that the council was in discussions with Brecon Beacons College, part of the NPTC Group of Colleges, to include them as a partner.
The Welsh Government and Heritage Lottery Fund have provided almost £4 million in grant funding for the project.