Sometime Today, Manish Jethani assembled some asciibets to say:
perl -ne 's/^Date## +(.+)$/$1/ && print $_' </root/sandeep/log111.txt
^^^^^^^^
That makes it inefficient (although, in this case only mildly so).
instead, try avoiding the back reference:
s/^Date##\s+// && print $_
Since you know that what's left on the line is all that you want.
Alternately, use a match: /^Date##\s+(.+)$/ && print $1
Philip