6, 7, 18, 63, 265, 1365

The given series is in the below pattern,
First term = 6
Second term = First term x 1 +1²
⇒ Second term = 6 x 1 + 1² = 6 + 1 = 7
Third term = Second term x 2 + 2²
⇒ Third term = 7 x 2 + 2² = 14 + 4 = 18
Fourth term = Third term x 3 + 3²
⇒ Fourth term = 18 x 3 + 3² = 54 + 9 = 63
Fifth term = Fourth term x 4 +4²
⇒ Fifth term = 63 x 4 + 4² = 252 + 16 = 265
So 265 is wrong. we get 268 as 5th term.
Sixth term = Fifth term x 5 + 5²
⇒ Sixth term = 268 x 5 + 5² = 1340 + 25 = 1365