A "constant" in google spreadsheet?

Short answer

Use an absolute cell reference or a named range

Explanation

Instead of E1, which is a relative cell reference, use $E$1 which is an absolute cell reference.

An alternative is to to assign a name to the cell E1, let say, "constant"

In the first case the formula will be

=A2*$E$1

In the second case

=A2*constant 

References

  • Spreadsheet - Wikipedia
  • Name a range of cells - Google Docs Editors Help

I understand that you are asking for "A “constant” in Google spreadsheet?" and later on a "drag down" solution.

You can use the accepted answer, OR ...
Instead of having to drag down (increasing the number of formulas)

Use a single formula in B2

=ArrayFormula(A2:A6*E1)  

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You can even use it for future entries or now blank cells.

=ArrayFormula(IF(A2:A11<>"",A2:A11*E1,""))

enter image description here

How the formula works

The ArrayFormula will apply the calculation cell*E1 in every single row, IF the cell is not empty/blank "".
IF it is a blank cell it will return a blank cell "".

Functions used:

  • ArrayFormula
  • IF