```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
torch::Tensor fused_pool_sum_cuda(torch::Tensor x);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/AccumulateType.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cmath>
#include <cstdint>

template <typename T>
__device__ __forceinline__ T nan_max(T a, T b) {
    return isnan(a) ? a : (isnan(b) ? b : (a > b ? a : b));
}

template <typename scalar_t>
__global__ void fused_pool_sum_kernel(
    const scalar_t* __restrict__ input,
    scalar_t* __restrict__ output,
    int64_t channels,
    int64_t depth,
    int64_t height,
    int64_t width,
    int64_t out_depth,
    int64_t out_height,
    int64_t out_width,
    int64_t output_count
) {
    using acc_t = at::acc_type<scalar_t, true>;
    constexpr int WARPS = 8;
    __shared__ acc_t partial[WARPS];

    const int lane = threadIdx.x & 31;
    const int warp = threadIdx.x >> 5;
    const int64_t spatial_count = out_depth * out_height * out_width;
    const int64_t channel_stride = depth * height * width;

    for (int64_t index = blockIdx.x;
         index < output_count;
         index += gridDim.x) {
        const int64_t batch = index / spatial_count;
        int64_t spatial = index % spatial_count;
        const int64_t ow = spatial % out_width;
        spatial /= out_width;
        const int64_t oh = spatial % out_height;
        const int64_t od = spatial / out_height;

        const int64_t origin =
            batch * channels * channel_stride +
            od * 6 * height * width +
            oh * 6 * width +
            ow * 6;

        acc_t channel_sum = acc_t(0);

        for (int64_t channel = warp; channel < channels; channel += WARPS) {
            const scalar_t* base = input + origin + channel * channel_stride;
            acc_t maximum = -static_cast<acc_t>(INFINITY);

            // Pooling by 2, then by 3, is a single disjoint 6x6x6 maximum.
            #pragma unroll
            for (int iteration = 0; iteration < 7; ++iteration) {
                const int position = lane + iteration * 32;
                if (position < 216) {
                    const int dz = position / 36;
                    const int dy = (position % 36) / 6;
                    const int dx = position % 6;
                    const acc_t value = static_cast<acc_t>(
                        base[dz * height * width + dy * width + dx]
                    );
                    maximum = nan_max(maximum, value);
                }
            }

            #pragma unroll
            for (int offset = 16; offset > 0; offset >>= 1) {
                maximum = nan_max(
                    maximum,
                    __shfl_down_sync(0xffffffff, maximum, offset)
                );
            }

            if (lane == 0) {
                channel_sum += maximum;
            }
        }

        if (lane == 0) {
            partial[warp] = channel_sum;
        }
        __syncthreads();

        if (threadIdx.x == 0) {
            acc_t result = acc_t(0);
            #pragma unroll
            for (int i = 0; i < WARPS; ++i) {
                result += partial[i];
            }
            output[index] = static_cast<scalar_t>(result);
        }
        __syncthreads();
    }
}

torch::Tensor fused_pool_sum_cuda(torch::Tensor x) {
    TORCH_CHECK(x.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(x.dim() == 5, "Expected NCDHW input");
    TORCH_CHECK(x.is_contiguous(), "Expected contiguous input");

    const c10::cuda::CUDAGuard device_guard(x.device());

    const int64_t n = x.size(0);
    const int64_t c = x.size(1);
    const int64_t d = x.size(2);
    const int64_t h = x.size(3);
    const int64_t w = x.size(4);
    const int64_t od = d / 6;
    const int64_t oh = h / 6;
    const int64_t ow = w / 6;

    TORCH_CHECK(c > 0 && od > 0 && oh > 0 && ow > 0,
                "Input is too small for the pooling operations");

    auto output = torch::empty({n, 1, od, oh, ow}, x.options());
    const int64_t count = output.numel();
    if (count == 0) {
        return output;
    }

    const int blocks = static_cast<int>(count < 65535 ? count : 65535);
    const auto stream = at::cuda::getCurrentCUDAStream();

    AT_DISPATCH_FLOATING_TYPES_AND2(
        at::ScalarType::Half,
        at::ScalarType::BFloat16,
        x.scalar_type(),
        "fused_pool_sum_cuda",
        [&] {
            fused_pool_sum_kernel<scalar_t><<<blocks, 256, 0, stream>>>(
                x.data_ptr<scalar_t>(),
                output.data_ptr<scalar_t>(),
                c, d, h, w, od, oh, ow, count
            );
        }
    );
    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_fused_ops = load_inline(
    name="fused_pool3d_2_3_channel_sum",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_pool_sum_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, stride, padding):
        super().__init__()
        self.conv_transpose = nn.ConvTranspose3d(
            in_channels,
            out_channels,
            kernel_size,
            stride=stride,
            padding=padding,
        )
        self.max_pool1 = nn.MaxPool3d(kernel_size=2)
        self.max_pool2 = nn.MaxPool3d(kernel_size=3)

    def forward(self, x):
        x = self.conv_transpose(x)
        if not x.is_cuda or (torch.is_grad_enabled() and x.requires_grad):
            return self.max_pool2(self.max_pool1(x)).sum(dim=1, keepdim=True)
        return _fused_ops.fused_pool_sum_cuda(x.contiguous())
```