The average of square of first 6 consecutive even numbers is:

60.66

Here,

Sum of square of first n consecutive even numbers =\(\frac{2n(n+1)(2n+1)}{3}\)

and

Average of square of first n consecutive even numbers =\(\frac{2n(n+1)(2n+1)}{3n}\) = \(\frac{2(n+1)(2n+1)}{3}\)

Thus,

Average of square of first 6 consecutive even numbers = \(\frac{2(6+1)(12+1)}{3}\) = \(\frac{(14)(13)}{3}\) = \(\frac{182}{3}\) = 60.66

OR

First 6 consecutive even numbers:  2, 4, 6, 8, 10, 12

Sum of square of 6 consecutive even numbers:  2² + 4² + 6² + 8² + 10² + 12² = 4 + 16 + 36 + 64 + 100 + 144 = 364

Average of the square of first 6 consecutive even numbers = \(\frac{ 364}{ 6}\)

Average of the square of first 6 consecutive even numbers = 60.66