diff --git a/Library/Homebrew/cask/dsl.rb b/Library/Homebrew/cask/dsl.rb
index d6c5d4ab12..b01b707083 100644
--- a/Library/Homebrew/cask/dsl.rb
+++ b/Library/Homebrew/cask/dsl.rb
@@ -310,19 +310,36 @@ module Cask
     # For architecture-dependent downloads:
     #
     # ```ruby
-    # sha256 arm:   "7bdb497080ffafdfd8cc94d8c62b004af1be9599e865e5555e456e2681e150ca",
-    #        intel: "b3c1c2442480a0219b9e05cf91d03385858c20f04b764ec08a3fa83d1b27e7b2"
-    #        linux: "1a2aee7f1ddc999993d4d7d42a150c5e602bc17281678050b8ed79a0500cc90f"
+    # sha256 arm:          "7bdb497080ffafdfd8cc94d8c62b004af1be9599e865e5555e456e2681e150ca",
+    #        x86_64:       "b3c1c2442480a0219b9e05cf91d03385858c20f04b764ec08a3fa83d1b27e7b2"
+    #        x86_64_linux: "1a2aee7f1ddc999993d4d7d42a150c5e602bc17281678050b8ed79a0500cc90f"
+    #        arm64_linux:  "bd766af7e692afceb727a6f88e24e6e68d9882aeb3e8348412f6c03d96537c75"
     # ```
     #
     # @api public
-    def sha256(arg = nil, arm: nil, intel: nil, linux: nil)
-      should_return = arg.nil? && arm.nil? && intel.nil? && linux.nil?
+    sig {
+      params(
+        arg:          T.nilable(T.any(String, Symbol)),
+        arm:          T.nilable(String),
+        intel:        T.nilable(String),
+        x86_64:       T.nilable(String),
+        x86_64_linux: T.nilable(String),
+        arm64_linux:  T.nilable(String),
+      ).returns(T.nilable(T.any(Symbol, Checksum)))
+    }
+    def sha256(arg = nil, arm: nil, intel: nil, x86_64: nil, x86_64_linux: nil, arm64_linux: nil)
+      should_return = arg.nil? && arm.nil? && (intel.nil? || x86_64.nil?) && x86_64_linux.nil? && arm64_linux.nil?
 
+      x86_64 ||= intel if intel.present? && x86_64.nil?
       set_unique_stanza(:sha256, should_return) do
-        @on_system_blocks_exist = true if arm.present? || intel.present? || linux.present?
+        if arm.present? || x86_64.present? || x86_64_linux.present? || arm64_linux.present?
+          @on_system_blocks_exist = true
+        end
 
-        val = arg || on_system_conditional(macos: on_arch_conditional(arm:, intel:), linux:)
+        val = arg || on_system_conditional(
+          macos: on_arch_conditional(arm:, intel: x86_64),
+          linux: on_arch_conditional(arm: arm64_linux, intel: x86_64_linux),
+        )
         case val
         when :no_check
           val
@@ -362,6 +379,12 @@ module Cask
     # ```
     #
     # @api public
+    sig {
+      params(
+        macos: T.nilable(String),
+        linux: T.nilable(String),
+      ).returns(T.nilable(String))
+    }
     def os(macos: nil, linux: nil)
       should_return = macos.nil? && linux.nil?