Get total files size from a file containing a file list

I have a file containing a list of files that I would like to know the total files size. Is there a command to do so?

My OS is a very basic linux (Qnap TS-410).

EDIT:

A few lines from the file:

/share/archive/Bailey Test/BD006/0.tga
/share/archive/Bailey/BD007/1 version 1.tga
/share/archive/Bailey 2/BD007/example.tga

I believe something like this would work in busybox:

du `cat filelist.txt` | awk '{i+=$1} END {print i}'

I don't have the same environment as you, but if you encounter issues with spaces in filenames something like this would work too:

cat filelist.txt | while read file;do
  du "$file"
done | awk '{i+=$1} END {print i}'

Edit 1:
@stew is right in his post below, du shows the disk usage and not the exact filesize. To change the behavior busybox uses the -a flag, so try: du -a "$file" for exact filesize and compare the output/behavior.

du -c `cat filelist.txt` | tail -1 | cut -f 1

-c adds line "total size";
tail -1 takes last line (with total size);
cut -f 1 cuts out word "total".

I don't know if your linux tools are capable of this, but:

cat /tmp/filelist.txt  |xargs -d \\n du -c

Do, the xargs will set the delimiter to be a newline character, and du will produce a grand total for you.

Looking at http://busybox.net/downloads/BusyBox.html it seems that "busybox du" will support the grand total option, but the "busybox xargs" will not support custom delimiters.

Again, I'm not sure of your toolset.