diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 8f3a599bf107c..9c58c01f833a3 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -547,7 +547,9 @@ def _binary_op_method_timedeltalike(op, name):
 
         try:
             other = Timedelta(other)
-        except ValueError:
+        except (ValueError, SystemError):
+            # catch SystemError to workaround NumPy issue
+            # https://github.com/numpy/numpy/issues/15502
             # failed to parse as timedelta
             return NotImplemented
 
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 8cef685933863..8f147d067cc84 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -205,10 +205,10 @@ def integer_op_not_supported(obj):
 
     # GH#30886 using an fstring raises SystemError
     int_addsub_msg = (
-        f"Addition/subtraction of integers and integer-arrays with {cls} is "
+        "Addition/subtraction of integers and integer-arrays with {cls} is "
         "no longer supported.  Instead of adding/subtracting `n`, "
         "use `n * obj.freq`"
-    )
+    ).format(cls=cls)
     return TypeError(int_addsub_msg)
 
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 3d2200cb45c6e..40fb2432d81bc 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8545,43 +8545,35 @@ def blk_func(values):
                 out[:] = coerce_to_dtypes(out.values, df.dtypes)
             return out
 
-        if not self._is_homogeneous_type:
-            # try to avoid self.values call
-
-            if filter_type is None and axis == 0 and len(self) > 0:
-                # operate column-wise
-
-                # numeric_only must be None here, as other cases caught above
-                # require len(self) > 0 bc frame_apply messes up empty prod/sum
-
-                # this can end up with a non-reduction
-                # but not always. if the types are mixed
-                # with datelike then need to make sure a series
-
-                # we only end up here if we have not specified
-                # numeric_only and yet we have tried a
-                # column-by-column reduction, where we have mixed type.
-                # So let's just do what we can
-                from pandas.core.apply import frame_apply
-
-                opa = frame_apply(
-                    self, func=f, result_type="expand", ignore_failures=True
-                )
-                result = opa.get_result()
-                if result.ndim == self.ndim:
-                    result = result.iloc[0].rename(None)
-                return result
-
         if numeric_only is None:
             data = self
             values = data.values
-
             try:
                 result = f(values)
 
             except TypeError:
                 # e.g. in nanops trying to convert strs to float
 
+                # try by-column first
+                if filter_type is None and axis == 0:
+                    # this can end up with a non-reduction
+                    # but not always. if the types are mixed
+                    # with datelike then need to make sure a series
+
+                    # we only end up here if we have not specified
+                    # numeric_only and yet we have tried a
+                    # column-by-column reduction, where we have mixed type.
+                    # So let's just do what we can
+                    from pandas.core.apply import frame_apply
+
+                    opa = frame_apply(
+                        self, func=f, result_type="expand", ignore_failures=True
+                    )
+                    result = opa.get_result()
+                    if result.ndim == self.ndim:
+                        result = result.iloc[0]
+                    return result
+
                 # TODO: why doesnt axis matter here?
                 data = _get_data(axis_matters=False)
                 labels = data._get_agg_axis(axis)
@@ -8589,7 +8581,6 @@ def blk_func(values):
                 values = data.values
                 with np.errstate(all="ignore"):
                     result = f(values)
-
         else:
             if numeric_only:
                 data = _get_data(axis_matters=True)
diff --git a/pandas/tests/arrays/integer/test_function.py b/pandas/tests/arrays/integer/test_function.py
index 44c3077228e80..c584fb9f704b8 100644
--- a/pandas/tests/arrays/integer/test_function.py
+++ b/pandas/tests/arrays/integer/test_function.py
@@ -133,6 +133,15 @@ def test_integer_array_numpy_sum(values, expected):
     assert result == expected
 
 
+def test_mixed_frame_with_integer_sum():
+    # https://github.com/pandas-dev/pandas/issues/34520
+    df = pd.DataFrame([["a", 1]], columns=list("ab"))
+    df = df.astype({"b": "Int64"})
+    result = df.sum()
+    expected = pd.Series(["a", 1], index=["a", "b"])
+    tm.assert_series_equal(result, expected)
+
+
 # TODO(jreback) - these need testing / are broken
 
 # shift
diff --git a/pandas/tests/frame/test_analytics.py b/pandas/tests/frame/test_analytics.py
index db8bb5ca3c437..e9af883a717b5 100644
--- a/pandas/tests/frame/test_analytics.py
+++ b/pandas/tests/frame/test_analytics.py
@@ -351,9 +351,7 @@ def kurt(x):
             "sum", np.sum, float_frame_with_na, skipna_alternative=np.nansum
         )
         assert_stat_op_calc("mean", np.mean, float_frame_with_na, check_dates=True)
-        assert_stat_op_calc(
-            "product", np.prod, float_frame_with_na, skipna_alternative=np.nanprod
-        )
+        assert_stat_op_calc("product", np.prod, float_frame_with_na)
 
         assert_stat_op_calc("mad", mad, float_frame_with_na)
         assert_stat_op_calc("var", var, float_frame_with_na)