A new BVA report released on Wednesday and seen by the Bild newspaper found that two pension funds had missed payments, in many case over several years.
The government agency investigated cases at two different insurance firms. After examining 3,289 cases at the Knappschaft-Bahn-See (KBS) insurer, the BVA found that 1,210 widows and widowers had not received child allowances they had been entitled to over several years.
An additional €2.9 million was expected to be sent out as result - some of these payments have already been made.
Meanwhile, the Rentenversicherung Bund (DRV), which operates Germany's state pension system, underpaid 7,992 pensioners, out of 26,045 cases examined. The payment of arrears would total €19.4 million - or an average €57.28 extra per month per pensioner affected.
The BVA also discovered tens of thousands of miscalculations when it came to contributions made during mid-career training periods. Of the 215,542 cases investigated across both pension funds, the government agency found that 147,702 (68.5 percent) people had been underpaid, while around 4,000 had received too much.
The DRV welcomed the report and said that the "appropriate measures" had been taken "to avoid similar cases in the future."
The new report only covers the KBS and the DRV - Germany's two national pension providers. The 14 regional funds, which hold almost of half of the country's pensions, are still being investigated.