Find out the missing term of the number series given below.

68, ?, 407, 470, 496, 503

The correct answer is 283.

To find the missing term in the number series 68, ?, 407, 470, 496, 503, let's analyze the differences between the consecutive known terms, starting from the right end of the series:

Difference between 503 and 496:
$503-496=7$

Difference between 496 and 470:
$496-470=26$

Difference between 470 and 407:
$470-407=63$

Now, let's look at the pattern of these differences: 7, 26, 63. These numbers are very close to perfect cubes ($n^3$):

$7=2^3-1=8-1$

$26=3^3-1=27-1$

$63=4^3-1=64-1$

Following this pattern ($n^3-1$), the preceding differences should be:

For the difference between 407 and the missing term (?):
$5^3-1=125-1=124$

For the difference between the missing term (?) and 68:
$6^3-1=216-1=215$

Let's check if we obtain the correct missing term using these differences:

Subtracting 124 from 407 gives:
$407-124=283$

Let's verify this value with the first term of the series (68):
$283-68=215$

This matches our expected difference of 215 ($6^3-1$). Therefore, the pattern is consistent throughout the series, and the missing number is 283.