The first term of a sequence is $2014$. Each succeeding term is the sum of the cubes of the digits of the previous term. What is the $2014$ th term of the sequence?
1. **Identify the first term of the sequence:**
   The first term is given as \(2014\).

2. **Calculate the second term:**
   The second term is the sum of the cubes of the digits of the first term.
   \[
   2^3 + 0^3 + 1^3 + 4^3 = 8 + 0 + 1 + 64 = 73
   \]

3. **Calculate the third term:**
   The third term is the sum of the cubes of the digits of the second term.
   \[
   7^3 + 3^3 = 343 + 27 = 370
   \]

4. **Calculate the fourth term:**
   The fourth term is the sum of the cubes of the digits of the third term.
   \[
   3^3 + 7^3 + 0^3 = 27 + 343 + 0 = 370
   \]

5. **Observe the pattern:**
   From the calculations, we see that once the sequence reaches \(370\), it remains constant:
   \[
   370, 370, 370, \ldots
   \]

6. **Determine the 2014th term:**
   Since the sequence stabilizes at \(370\) from the third term onwards, the 2014th term will also be \(370\).

The final answer is \(\boxed{370}\).