CAN1 loopback does not work on STM32F427

Segment 1 should be larger than Segment 2. Use this online calculator http://www.bittiming.can-wiki.info/

I did some test with your code and found an issue. If you're using polling method then don't use HAL_CAN_ActivateNotification else you'll get stuck in while(HAL_CAN_IsTxMessagePending(&hcan1, TxMailbox));

Here is what I did to get either Interrupt or Polling method to work. Interrupt mode blinks the LED fast while polling blinks the LED slowly. I moved your code out of main.c and created separate functions.

main.c

 /* Infinite loop */
 /* USER CODE BEGIN WHILE */
 PollingInit();
 while (1)
 {
	 PollingRoutine();
 /* USER CODE END WHILE */

 /* USER CODE BEGIN 3 */
 }
 /* USER CODE END 3 */

PollingRoutine.c

/*
 * PollingRoutine.c
 *
 * Created on: Oct 24, 2023
 * Author: karl.yamashita
 *
 *
 * Template for projects.
 *
 */


#include "main.h"


//#define USE_CAN_INTERRUPT


extern CAN_HandleTypeDef hcan1;


CAN_TxHeaderTypeDef TxHeader;
CAN_RxHeaderTypeDef RxHeader;
uint8_t TxData[8];
uint8_t RxData[8];
uint32_t TxMailbox;
bool CAN_MsgRdy = false;


void PollingInit(void)
{
	CAN_FilterInit();
}

void PollingRoutine(void)
{
	CAN_SendTxMessage();
#ifdef USE_CAN_INTERRUPT
	CAN_CheckMsg();
#else
	CAN_ReceiveMessage();
#endif
	HAL_Delay(100);
}

void led1_on(void)
{
	HAL_GPIO_WritePin(LD3_GPIO_Port, LD3_Pin, GPIO_PIN_SET);
}

void led1_off(void)
{
	HAL_GPIO_WritePin(LD3_GPIO_Port, LD3_Pin, GPIO_PIN_RESET);
}


void CAN_FilterInit(void)
{
	CAN_FilterTypeDef CAN1_Filter;

	CAN1_Filter.FilterBank = 0;
	CAN1_Filter.FilterMode = CAN_FILTERMODE_IDMASK;
	CAN1_Filter.FilterScale = CAN_FILTERSCALE_32BIT;
	CAN1_Filter.FilterIdHigh = 0x0000;
	CAN1_Filter.FilterIdLow = 0x0000;
	CAN1_Filter.FilterMaskIdHigh = 0x0000;
	CAN1_Filter.FilterMaskIdLow = 0x0000;
	CAN1_Filter.FilterFIFOAssignment = CAN_RX_FIFO0;
	CAN1_Filter.FilterActivation = ENABLE;
	CAN1_Filter.SlaveStartFilterBank = 14;

	if (HAL_CAN_ConfigFilter(&hcan1, &CAN1_Filter) != HAL_OK)
	{
	 Error_Handler();
	}

	if (HAL_CAN_Start(&hcan1) != HAL_OK)
	{
	 Error_Handler();
	}
#ifdef USE_CAN_INTERRUPT
	if (HAL_CAN_ActivateNotification(&hcan1, CAN_IT_RX_FIFO0_MSG_PENDING | CAN_IT_TX_MAILBOX_EMPTY | CAN_IT_ERROR) != HAL_OK)
	{
	 Error_Handler();
	}
#endif
}

void CAN_SendTxMessage(void)
{
	TxHeader.StdId = 0x11;
	TxHeader.RTR = CAN_RTR_DATA;
	TxHeader.IDE = CAN_ID_STD;
	TxHeader.DLC = 2;
	TxHeader.TransmitGlobalTime = DISABLE;
	TxData[0] = 0xCA;
	TxData[1] = 0xFE;

	if (HAL_CAN_AddTxMessage(&hcan1, &TxHeader, TxData, &TxMailbox) != HAL_OK)
	{
	 Error_Handler();
	}
}

#ifdef USE_CAN_INTERRUPT
void HAL_CAN_RxFifo0MsgPendingCallback(CAN_HandleTypeDef *hcan)
{
	// currently not used as we use polling for test purposes
	if(hcan == &hcan1)
	{
		if (HAL_CAN_GetRxMessage(&hcan1, CAN_RX_FIFO0, &RxHeader, RxData) != HAL_OK)
		{
		 Error_Handler();
		}
		CAN_MsgRdy = true;
	}
}

void CAN_CheckMsg(void)
{
	if(CAN_MsgRdy)
	{
		CAN_MsgRdy = false;
		if(RxHeader.StdId == 0x11)
		{
			if((RxData[0]<<8 | RxData[1]) == 0xCAFE)
			{
				led1_on();
				HAL_Delay(100);
				led1_off();
				HAL_Delay(100);
			}
		}
	}
}

#else // Polling
void CAN_ReceiveMessage(void)
{
	while(HAL_CAN_IsTxMessagePending(&hcan1, TxMailbox));
	while(HAL_CAN_GetTxMailboxesFreeLevel(&hcan1) != 3);

	HAL_Delay(20);

	if (HAL_CAN_GetRxFifoFillLevel(&hcan1, CAN_RX_FIFO0) != 1)
	{
	 Error_Handler();
	}

	if (HAL_CAN_GetRxMessage(&hcan1, CAN_RX_FIFO0, &RxHeader, RxData) != HAL_OK)
	{
	 Error_Handler();
	}

	if(RxHeader.StdId == 0x11)
	{
		if((RxData[0]<<8 | RxData[1]) == 0xCAFE)
		{
			led1_on();
			HAL_Delay(500);
			led1_off();
			HAL_Delay(500);
		}
	}
}
#endif

Thanks to both of you, both answers were very helpful!

With the bit timing provided by @mƎALLEm, the TX no longer failed. With the code from @Karl Yamashita , the reception also worked.