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Answer: $6000$


$\underbrace{\overbrace{12345}^{15}\overbrace{12345}^{15}\overbrace{12345}^{15}\dots\overbrace{12345}^{15}}_\text{2000 digits}$

Total: $15\times(2000\div5) = 6000$


Alternatively, the mean of each group of five digits is $3$ and so the mean of the digits making up the number is $3$. Therefore the sum is $2000\times 3=6000$.
Note that this only works because the groups are in $5$s, and $5$ goes into $2000$ exactly

 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.