Is there a shortcut method to calculate the Steric Number?
Short answer: no.


The steric number is a property of an atom, not a compound. You need to know what an atom connected to a given atom to know its steric number. For simple compounds, you can usually determine these connections because the formula suggests a central atom and surrounding groups. For hydrocarbons and other organic compounds, you need to consider isomerism. Given the capability of carbon to form complicated bonding patterns, even simple formulas can produce a fair number of isomers with different bonding patterns and steric numbers. 


  Let's look at some examples.


$\ce{C4H10}$

This formula corresponds to two compounds with the structures shown:



In this case, both compounds have all four carbon atoms with steric number of 4.

it is not always true that a set of hydrocarbon isomers will always have the same steric number for all carbon atoms or even the same set of steric numbers.

$\ce{C4H8}$

This formula corresponds to six isomers:



Note that four of these structures have two carbon atoms with steric number 4 and two carbon atoms with steric number 3. The other two have all four carbon atoms with steric number 4. 

Any method to calculate steric number for carbon atoms in an organic compound using just the formula will fail. You must examine the structure.