Let C be the number of lion cubs.
There are 2C meerkats in the new exhibit.
The zoo sent 4 gorillas away, so they had 68 - 6 = <<68-6=62>>62 animals left.
They adopted a hippopotamus, so they had 62 + 1 = <<62+1=63>>63 animals.
They took in 3 rhinos, so they had 63 + 3 = <<63+3=66>>66 animals.
Thus, they had 90 - 66 = <<90-66=24>>24 new lion cubs and meerkats.
Therefore, they had C + 2C = 3C = 24 new lion cubs as meerkats.
Hence, there were C = 24 / 3 = <<24/3=8>>8 lion cubs born.
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