How can I draw this multilayer heat sink using solidworks?

Step 1- Create an 'Extruded Boss/Base' feature of the rectangular block defined by the L,W,H dimensions

Step 2- Make an 'Extruded Cut' feature for the opening defined by the a,b dimensions

Step 3- Create a 'Linear Pattern' feature to pattern the extruded cut from step 2 in the y and z directions. a+w = the z direction pattern increment, and b+t = the y direction pattern increment.

why ? constrain yourself to solidworks. Might - i suggest you look at some of the open source heat sink design software. Think outside the box. A lot of these free alternatives out perform the more expensive applications. Or in some case a small fee. Don't restrict your self to one product or application.