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

68, ?, 407, 470, 496, 503

To find the missing term of the number series, let us analyze the differences between consecutive terms in the series:
68, ?, 407, 470, 496, 503

Let us look at the differences between the known adjacent terms at the 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:
$470-407=63$

Let us examine the pattern of these differences: 7, 26, and 63. These numbers are very close to perfect cubes:
$7=2^3-1$ (since $2^3=8$)
$26=3^3-1$ (since $3^3=27$)
$63=4^3-1$ (since $4^3=64$)

Following this logic, the differences between consecutive terms represent the pattern of $n^3-1$ in descending order as we move leftwards.
Let us write the complete sequence of differences from left to right:
1. First difference (between 68 and the missing term): $6^3-1=216-1=215$
2. Second difference (between the missing term and 407): $5^3-1=125-1=124$
3. Third difference (between 407 and 470): $4^3-1=64-1=63$ (which matches)
4. Fourth difference (between 470 and 496): $3^3-1=27-1=26$ (which matches)
5. Fifth difference (between 496 and 503): $2^3-1=8-1=7$ (which matches)

Let us calculate the missing term by adding the first difference to 68:
$68+215=283$

Let us verify if this missing term fits with the next term (407):
$283+124=407$

The calculation is consistent and verified. Thus, the missing term is 283.