The birds, which are native to southern Europe, set up nests by burrowing tunnels in the banks of Low Gelt Quarry, near Brampton.
An RSPB viewpoint on the perimeter of the quarry has attracted more than 1,000 people in two weeks.
The RSPB said all chicks had hatched and would fledge in the next few weeks.
The pairs were discovered by a foreman, who noticed the colourful birds flying among the site's colony of nesting sand martins. They are expected to leave the nest in about four weeks.
Two pairs successfully raised chicks on the Isle of Wight last year and previously in County Durham in 2002.
An RSPB spokesman said they were "delighted" the birds had bred in the UK for a second consecutive summer.
Bee-eaters can burrow up to 10ft (3m) and usually lay clutches of four to nine eggs.
Visitors have flocked to Cumbria to see two pairs of rare bee-eater birds which set up their home at a quarry.