Problem (Algebra):
The first term of a sequence is 2007. Each term, starting with the second, is the sum of the cubes of the digits of the previous term. What is the 2007th term?

Solution:
From the given information, the first term in the sequence is 2007 and each term starting with the second can be determined from the previous term.

The second term is $2^{3}+0^{3}+0^{3}+7^{3}=8+0+0+343=351$.

The third term is $3^{3}+5^{3}+1^{3}=27+125+1=153$.

The fourth term is $1^{3}+5^{3}+3^{3}=27+125+1=153$.

Since two consecutive terms are equal, then every term thereafter will be equal, because each term depends only on the previous term and a term of 153 always makes the next term 153.

Thus, the 2007th term will be 153 .

Final answer: 153