Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the chocolate cake mix, water, vegetable oil, and eggs. Beat with a hand mixer on medium speed for about 2 minutes until well combined.
Add the shredded coconut and chopped strawberries to the batter. Mix gently until incorporated.
Pour the cake batter into the greased 9x13 inch baking dish and spread it evenly.
In another bowl, beat the softened cream cheese with the powdered sugar and vanilla extract until smooth and creamy.
Drop spoonfuls of the cream cheese mixture over the chocolate cake batter. Use a knife or toothpick to swirl the cream cheese into the cake batter, creating a marbled effect.
If using, sprinkle the chopped pecans or walnuts on top of the cake.
Bake in the preheated oven for 40-45 minutes or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 15 minutes before slicing and serving.
For a stronger strawberry flavor, feel free to add more chopped strawberries to the cream cheese mixture.
You can serve this cake warm, or it can be refrigerated and enjoyed chilled.
This cake pairs well with whipped cream or a scoop of vanilla ice cream.